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An exact multiplicity result for a class of semilinear equations
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An exact multiplicity result for a class of semilinear equations

Author: Tiancheng Ouyang Affiliation: Brigham Young Univ., Provo, UT (United States)
Edition/Format: Article Article : English
Publication:Communications in Partial Differential Equations, v22 n3-4 (19971101): 661-684
Summary:
For a class of Dirichlet problems in two dimensions, generalizing the model case we show existence, of a critical λ0 > 0, so that there are exactly 0, 1 or 2 nontrivial solutions (in fact, positive), depending on Whether λ < λ0, λ = λ0 or λ > λ0. We show that all solutions lie on a single smooth solution curve, and study sonic properties of this curve. We use bifurcation approach. The crucial thing is to show that any nontrivial solution of the corresponding linearizes problem is of one sign. 14 refs.  Read more...
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Details

Document Type: Article
All Authors / Contributors: Tiancheng Ouyang Affiliation: Brigham Young Univ., Provo, UT (United States)
Language Note: English
Unique Identifier: 4433217739
Notes: PBD: 1997
Journal ID: CPDIDZ
TRN: 97:003860-0012
Awards:

Abstract:

For a class of Dirichlet problems in two dimensions, generalizing the model case we show existence, of a critical λ0 > 0, so that there are exactly 0, 1 or 2 nontrivial solutions (in fact, positive), depending on Whether λ < λ0, λ = λ0 or λ > λ0. We show that all solutions lie on a single smooth solution curve, and study sonic properties of this curve. We use bifurcation approach. The crucial thing is to show that any nontrivial solution of the corresponding linearizes problem is of one sign. 14 refs.

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