Motreanu, D.
Overview
Works:  19 works in 71 publications in 2 languages and 1,489 library holdings 

Roles:  Author 
Classifications:  QA316, 515.64 
Publication Timeline
.
Most widely held works by
D Motreanu
Nonsmooth variational problems and their inequalities : comparison principles and applications by
S Carl(
Book
)
17 editions published between 2007 and 2011 in English and held by 190 WorldCat member libraries worldwide
"This monograph focuses primarily on nonsmooth variational problems that arise from boundary value problems with nonsmooth data and/or nonsmooth constraints, such as multivalued elliptic problems, variational inequalities, hemivariational inequalities, and their corresponding evolution problems." "This text is an invaluable reference for researchers and graduate students in mathematics (functional analysis, partial differential equations, elasticity, applications in materials science and mechanics) as well as physicists and engineers."Jacket
17 editions published between 2007 and 2011 in English and held by 190 WorldCat member libraries worldwide
"This monograph focuses primarily on nonsmooth variational problems that arise from boundary value problems with nonsmooth data and/or nonsmooth constraints, such as multivalued elliptic problems, variational inequalities, hemivariational inequalities, and their corresponding evolution problems." "This text is an invaluable reference for researchers and graduate students in mathematics (functional analysis, partial differential equations, elasticity, applications in materials science and mechanics) as well as physicists and engineers."Jacket
Tangency, flow invariance for differential equations, and optimization problems by
D Motreanu(
Book
)
9 editions published in 1999 in English and held by 149 WorldCat member libraries worldwide
9 editions published in 1999 in English and held by 149 WorldCat member libraries worldwide
Handbook of nonconvex analysis and applications(
Book
)
4 editions published in 2010 in English and held by 100 WorldCat member libraries worldwide
4 editions published in 2010 in English and held by 100 WorldCat member libraries worldwide
Minimax theorems and qualitative properties of the solutions of hemivariational inequalities by
D Motreanu(
Book
)
9 editions published between 1999 and 2014 in English and held by 98 WorldCat member libraries worldwide
The present book is the first ever published in which a new type of eigenvalue problem is studied, one that is very useful for applications: eigenvalue problems related to hemivariational inequalities, i.e. involving nonsmooth, nonconvex, energy functions. New existence, multiplicity and perturbation results are proved using three different approaches: minimization, minimax methods and (sub)critical point theory. Nonresonant and resonant cases are studied both for static and dynamic problems and several new qualitative properties of the hemivariational inequalities are obtained. Both simple and double eigenvalue problems are studied, as well as those constrained on the sphere and those which are unconstrained. The book is selfcontained, is written with the utmost possible clarity and contains highly original results. Applications concerning new stability results for beams, plates and shells with adhesive supports, etc. illustrate the theory. Audience: applied and pure mathematicians, civil, aeronautical and mechanical engineers
9 editions published between 1999 and 2014 in English and held by 98 WorldCat member libraries worldwide
The present book is the first ever published in which a new type of eigenvalue problem is studied, one that is very useful for applications: eigenvalue problems related to hemivariational inequalities, i.e. involving nonsmooth, nonconvex, energy functions. New existence, multiplicity and perturbation results are proved using three different approaches: minimization, minimax methods and (sub)critical point theory. Nonresonant and resonant cases are studied both for static and dynamic problems and several new qualitative properties of the hemivariational inequalities are obtained. Both simple and double eigenvalue problems are studied, as well as those constrained on the sphere and those which are unconstrained. The book is selfcontained, is written with the utmost possible clarity and contains highly original results. Applications concerning new stability results for beams, plates and shells with adhesive supports, etc. illustrate the theory. Audience: applied and pure mathematicians, civil, aeronautical and mechanical engineers
Variational and nonvariational methods in nonlinear analysis and boundary value problems by
D Motreanu(
Book
)
9 editions published between 2003 and 2011 in English and held by 94 WorldCat member libraries worldwide
The book provides a comprehensive exposition of modern topics in nonlinear analysis with applications to various boundary value problems with discontinuous nonlinearities and nonsmooth constraints. Our framework includes multivalued elliptic problems with discontinuities, variational inequalities, hemivariational inequalities and evolution problems. In addition to the existence of solutions, a major part of the book is devoted to the study of different qualitative properties such as multiplicity, location, extremality, and stability. The treatment relies on variational methods, monotonicity principles, topological arguments and optimization techniques. The book is based on the authors' original results obtained in the last decade. A great deal of the material is published for the first time in this book and is organized in a unifying way. The book is selfcontained. The abstract results are illustrated through various examples and applications
9 editions published between 2003 and 2011 in English and held by 94 WorldCat member libraries worldwide
The book provides a comprehensive exposition of modern topics in nonlinear analysis with applications to various boundary value problems with discontinuous nonlinearities and nonsmooth constraints. Our framework includes multivalued elliptic problems with discontinuities, variational inequalities, hemivariational inequalities and evolution problems. In addition to the existence of solutions, a major part of the book is devoted to the study of different qualitative properties such as multiplicity, location, extremality, and stability. The treatment relies on variational methods, monotonicity principles, topological arguments and optimization techniques. The book is based on the authors' original results obtained in the last decade. A great deal of the material is published for the first time in this book and is organized in a unifying way. The book is selfcontained. The abstract results are illustrated through various examples and applications
Variational and hemivariational inequalities : theory, methods, and applications(
Book
)
2 editions published in 2003 in English and held by 50 WorldCat member libraries worldwide
2 editions published in 2003 in English and held by 50 WorldCat member libraries worldwide
Topological and variational methods with applications to nonlinear boundary value problems by
D Motreanu(
Book
)
7 editions published in 2014 in English and held by 26 WorldCat member libraries worldwide
This book focuses on nonlinear boundary value problems and the aspects of nonlinear analysis which are necessary to their study. The authors first give a comprehensive introduction to the many different classical methods from nonlinear analysis, variational principles, and Morse theory. They then provide a rigorous and detailed treatment of the relevant areas of nonlinear analysis with new applications to nonlinear boundary value problems for both ordinary and partial differential equations. Recent results on the existence and multiplicity of critical points for both smooth and nonsmooth functional, developments on the degree theory of monotone type operators, nonlinear maximum and comparison principles for pLaplacian type operators, and new developments on nonlinear Neumann problems involving nonhomogeneous differential operator appears for the first time in book form. The presentation is systematic, and an extensive bibliography and a remarks section at the end of each chapter highlight the text. This work will serve as an invaluable reference for researchers working in nonlinear analysis and partial differential equations as well as a useful tool for all those interested in the topics presented
7 editions published in 2014 in English and held by 26 WorldCat member libraries worldwide
This book focuses on nonlinear boundary value problems and the aspects of nonlinear analysis which are necessary to their study. The authors first give a comprehensive introduction to the many different classical methods from nonlinear analysis, variational principles, and Morse theory. They then provide a rigorous and detailed treatment of the relevant areas of nonlinear analysis with new applications to nonlinear boundary value problems for both ordinary and partial differential equations. Recent results on the existence and multiplicity of critical points for both smooth and nonsmooth functional, developments on the degree theory of monotone type operators, nonlinear maximum and comparison principles for pLaplacian type operators, and new developments on nonlinear Neumann problems involving nonhomogeneous differential operator appears for the first time in book form. The presentation is systematic, and an extensive bibliography and a remarks section at the end of each chapter highlight the text. This work will serve as an invaluable reference for researchers working in nonlinear analysis and partial differential equations as well as a useful tool for all those interested in the topics presented
Variational amd hemivariational inequalities : theory, methods and applications. 2, Unilateral problems(
Book
)
1 edition published in 2003 in English and held by 6 WorldCat member libraries worldwide
1 edition published in 2003 in English and held by 6 WorldCat member libraries worldwide
Variational and hemivariational inequalities. theory, methods and applications by
Mohamed Rochdi(
Book
)
2 editions published in 2003 in English and held by 4 WorldCat member libraries worldwide
2 editions published in 2003 in English and held by 4 WorldCat member libraries worldwide
Quasi tangent vectors in flowinvariance and optimization problems on Bana h manifolds by
D Motreanu(
Book
)
2 editions published between 1980 and 1981 in English and held by 2 WorldCat member libraries worldwide
2 editions published between 1980 and 1981 in English and held by 2 WorldCat member libraries worldwide
Nonsmooth Variational Problems and Their Inequalities : Comparison Principles and Applications(
)
1 edition published in 2007 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 2007 in English and held by 2 WorldCat member libraries worldwide
Unilateral analysis and unilateral mechanics by
Mohamed Rochdi(
Book
)
1 edition published in 2003 in English and held by 2 WorldCat member libraries worldwide
This book includes a selfcontained theory of inequality problems and their applications to unilateral mechanics. Fundamental theoretical results and related methods of analysis are discussed on various examples and applications in mechanics. The work can be seen as a book of applied nonlinear analysis entirely devoted to the study of inequality problems, i.e. variational inequalities and hemivariational inequalities in mathematical models and their corresponding applications to unilateral mechanics. It contains a systematic investigation of the interplay between theoretical results and concrete problems in mechanics. It is the first textbook including a comprehensive and systematic study of both elliptic, parabolic and hyperbolic inequality models, dynamical unilateral systems and unilateral eigenvalues problems. The book is selfcontained and it offers, for the first time, the possibility to learn about inequality models and to acquire the essence of the theory in a relatively short time
1 edition published in 2003 in English and held by 2 WorldCat member libraries worldwide
This book includes a selfcontained theory of inequality problems and their applications to unilateral mechanics. Fundamental theoretical results and related methods of analysis are discussed on various examples and applications in mechanics. The work can be seen as a book of applied nonlinear analysis entirely devoted to the study of inequality problems, i.e. variational inequalities and hemivariational inequalities in mathematical models and their corresponding applications to unilateral mechanics. It contains a systematic investigation of the interplay between theoretical results and concrete problems in mechanics. It is the first textbook including a comprehensive and systematic study of both elliptic, parabolic and hyperbolic inequality models, dynamical unilateral systems and unilateral eigenvalues problems. The book is selfcontained and it offers, for the first time, the possibility to learn about inequality models and to acquire the essence of the theory in a relatively short time
Analiza variationala cu aplicatii in probleme eliptice by
D Motreanu(
Book
)
1 edition published in 1996 in Romanian and held by 1 WorldCat member library worldwide
1 edition published in 1996 in Romanian and held by 1 WorldCat member library worldwide
Multiplicity of solutions for a class of nonsymmetric eigenvalue hemivariational inequalities by Claudiu Ciulcu(
)
1 edition published in 2003 in English and held by 1 WorldCat member library worldwide
The aim of this paper is to establish the influence of a nonsymmetric perturbation for a symmetric hemivariational eigenvalue inequality with constraints. The original problem was studied by Goeleven et al. (Math. Methods Appl. Sci. 1997; 20: 548) who deduced the existence of infinitely many solutions for the symmetric case. In this paper it is shown that the number of solutions of the perturbed problem becomes larger and larger if the perturbation tends to zero with respect to a natural topology. The approach relies on topological methods in nonsmooth critical point theory leading to this new multiplicity information
1 edition published in 2003 in English and held by 1 WorldCat member library worldwide
The aim of this paper is to establish the influence of a nonsymmetric perturbation for a symmetric hemivariational eigenvalue inequality with constraints. The original problem was studied by Goeleven et al. (Math. Methods Appl. Sci. 1997; 20: 548) who deduced the existence of infinitely many solutions for the symmetric case. In this paper it is shown that the number of solutions of the perturbed problem becomes larger and larger if the perturbation tends to zero with respect to a natural topology. The approach relies on topological methods in nonsmooth critical point theory leading to this new multiplicity information
Existence results for inequality problems with lack of convexity by
D Motreanu(
)
1 edition published in 2000 in English and held by 1 WorldCat member library worldwide
We establish several existence results of HartmanStampacchia type for hemivariational inequalities on bounded and convex sets in a real reflexive Banach space. We also study the cases of coercive and noncoercive variationalhemivariational inequalities. Two applications on nonmonotone laws in networks and nonconvex semipermeability illustrate the abstract results
1 edition published in 2000 in English and held by 1 WorldCat member library worldwide
We establish several existence results of HartmanStampacchia type for hemivariational inequalities on bounded and convex sets in a real reflexive Banach space. We also study the cases of coercive and noncoercive variationalhemivariational inequalities. Two applications on nonmonotone laws in networks and nonconvex semipermeability illustrate the abstract results
Eigenvalue problems for degenerate nonlinear elliptic equations in anisotropic media by
D Motreanu(
)
1 edition published in 2005 in English and held by 1 WorldCat member library worldwide
We study nonlinear eigenvalue problems of the form ${\rm div}(a(x) \nabla u) = g(\lambda,x,u)$ in ${\Bbb R}^N$, where $a(x)$ is a degenerate nonnegative weight. We establish the existence of solutions and we obtain information on the multiplicity and location of solutions. Our approach is based on critical point theory in weighted Sobolev spaces combined with a CaffarelliKohnNirenberg type inequality. A specific minimax method is developed without making use of the PalaisSmale condition
1 edition published in 2005 in English and held by 1 WorldCat member library worldwide
We study nonlinear eigenvalue problems of the form ${\rm div}(a(x) \nabla u) = g(\lambda,x,u)$ in ${\Bbb R}^N$, where $a(x)$ is a degenerate nonnegative weight. We establish the existence of solutions and we obtain information on the multiplicity and location of solutions. Our approach is based on critical point theory in weighted Sobolev spaces combined with a CaffarelliKohnNirenberg type inequality. A specific minimax method is developed without making use of the PalaisSmale condition
Weak solutions of quasilinear problems with nonlinear boundary condition by FloricaCorina Crstea(
)
1 edition published in 2001 in English and held by 1 WorldCat member library worldwide
Let $\Omega\subset \Bbb R^N$ be an unbounded domain with (possible noncompact)smooth boundary $\Gamma$ and $n$ is the unit outward normal on $\Gamma$. At certain (extensive) assumptions there is proved the existence of solutions for the boundary value problem $$\text{div}(a(x)[vertical\nabla u[vertical^{p  2}\nabla u) = \lambda(1+[verticalx[vertical)^{\alpha_1}[verticalu[vertical^{p 2}u+ (1+[verticalx[vertical)^{\alpha_2}[verticalu[vertical^{q 2}u\quad \text{in }\Omega,$$ $$a(x)[vertical\nabla u[vertical^{p 2}\nabla u \cdot n + b(x)[verticalu[vertical^{p2} u = g(x, u) \quad \text{on }\Gamma.$$ Under more simple assumptions, the existence of eigensolutions for the eigenvalue problem $$ \text{div}(a(x)[vertical\nabla u[vertical^{p 2} \nabla u) = \lambda[(1+[verticalx[vertical^{\alpha_1})[verticalp[vertical^{p2} u+(1+[verticalx[vertical)^{\alpha_2}[verticalu[vertical^{q 2}u]\quad \text{in } \Omega,$$ $$a(x)[vertical\nabla u[vertical^{p 2}\nabla u\cdot n+ b(x)[verticalu[vertical^{p 2}u =\lambda g(x,u)\quad\text{on }\Gamma$$ is proved
1 edition published in 2001 in English and held by 1 WorldCat member library worldwide
Let $\Omega\subset \Bbb R^N$ be an unbounded domain with (possible noncompact)smooth boundary $\Gamma$ and $n$ is the unit outward normal on $\Gamma$. At certain (extensive) assumptions there is proved the existence of solutions for the boundary value problem $$\text{div}(a(x)[vertical\nabla u[vertical^{p  2}\nabla u) = \lambda(1+[verticalx[vertical)^{\alpha_1}[verticalu[vertical^{p 2}u+ (1+[verticalx[vertical)^{\alpha_2}[verticalu[vertical^{q 2}u\quad \text{in }\Omega,$$ $$a(x)[vertical\nabla u[vertical^{p 2}\nabla u \cdot n + b(x)[verticalu[vertical^{p2} u = g(x, u) \quad \text{on }\Gamma.$$ Under more simple assumptions, the existence of eigensolutions for the eigenvalue problem $$ \text{div}(a(x)[vertical\nabla u[vertical^{p 2} \nabla u) = \lambda[(1+[verticalx[vertical^{\alpha_1})[verticalp[vertical^{p2} u+(1+[verticalx[vertical)^{\alpha_2}[verticalu[vertical^{q 2}u]\quad \text{in } \Omega,$$ $$a(x)[vertical\nabla u[vertical^{p 2}\nabla u\cdot n+ b(x)[verticalu[vertical^{p 2}u =\lambda g(x,u)\quad\text{on }\Gamma$$ is proved
Variational and hemivariational inequalities. theory, methods, and applications by
D Goeleven(
)
1 edition published in 2003 in English and held by 0 WorldCat member libraries worldwide
1 edition published in 2003 in English and held by 0 WorldCat member libraries worldwide
Nonsmooth Variational Problems and Their Inequalities: Comparison Principles and Applications. Springer Monographs in Mathematics(
)
1 edition published in 2007 in English and held by 0 WorldCat member libraries worldwide
This monograph focuses primarily on nonsmooth variational problems that arise from boundary value problems with nonsmooth data and/or nonsmooth constraints, such as is multivalued elliptic problems, variational inequalities, hemivariational inequalities, and their corresponding evolution problems. The main purpose of this book is to provide a systematic and unified exposition of comparison principles based on a suitably extended subsupersolution method. This method is an effective and flexible technique to obtain existence and comparison results of solutions. Also, it can be employed for the investigation of various qualitative properties, such as location, multiplicity and extremality of solutions. In the treatment of the problems under consideration a wide range of methods and techniques from nonlinear and nonsmooth analysis is applied, a brief outline of which has been provided in a preliminary chapter in order to make the book selfcontained.; This text is an invaluable reference for researchers and graduate students in mathematics (functional analysis, partial differential equations, elasticity, applications in materials science and mechanics) as well as physicists and engineers
1 edition published in 2007 in English and held by 0 WorldCat member libraries worldwide
This monograph focuses primarily on nonsmooth variational problems that arise from boundary value problems with nonsmooth data and/or nonsmooth constraints, such as is multivalued elliptic problems, variational inequalities, hemivariational inequalities, and their corresponding evolution problems. The main purpose of this book is to provide a systematic and unified exposition of comparison principles based on a suitably extended subsupersolution method. This method is an effective and flexible technique to obtain existence and comparison results of solutions. Also, it can be employed for the investigation of various qualitative properties, such as location, multiplicity and extremality of solutions. In the treatment of the problems under consideration a wide range of methods and techniques from nonlinear and nonsmooth analysis is applied, a brief outline of which has been provided in a preliminary chapter in order to make the book selfcontained.; This text is an invaluable reference for researchers and graduate students in mathematics (functional analysis, partial differential equations, elasticity, applications in materials science and mechanics) as well as physicists and engineers
more
fewer
Audience Level
0 

1  
Kids  General  Special 
Related Identities
Associated Subjects
Boundary value problems Calculus of variations Differential equations Differential equations, Nonlinear Differential equations, Partial Flows (Differentiable dynamical systems) Functional analysis Functions, Special Hemivariational inequalities Mathematical optimization Mathematics Maxima and minima Mechanics Mechanics, Analytic Nonlinear boundary value problems Nonlinear functional analysis Nonlinear operators Nonlinear theories Nonsmooth optimization Operator theory Topological groups Variational inequalities (Mathematics)