On multiple solutions of a nonlinear Dirichlet problem

Alfonso Castro; Jorge Cossio; John M. Neuberger

doi:10.1016/S0362-546X(96)00240-4

On multiple solutions of a nonlinear Dirichlet problem

Alfonso Castro, Jorge Cossio, John M. Neuberger

Research output: Contribution to journal › Article › peer-review

10 Scopus citations

Abstract

We prove that a semilinear elliptic boundary value problem has five solutions when the range of the derivative of the nonlinearity includes at least the first two eigenvalues. We also prove that if the region is a ball the semilinear elliptic problem has two solutions that change sign and are nonradial.

Original language	English (US)
Pages (from-to)	3657-3662
Number of pages	6
Journal	Nonlinear Analysis, Theory, Methods and Applications
Volume	30
Issue number	6
DOIs	https://doi.org/10.1016/S0362-546X(96)00240-4
State	Published - Dec 1997
Externally published	Yes

Keywords

Multiplicity of solutions
Nonlinear Dirichlet problem

ASJC Scopus subject areas

Analysis
Applied Mathematics

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title = "On multiple solutions of a nonlinear Dirichlet problem",

abstract = "We prove that a semilinear elliptic boundary value problem has five solutions when the range of the derivative of the nonlinearity includes at least the first two eigenvalues. We also prove that if the region is a ball the semilinear elliptic problem has two solutions that change sign and are nonradial.",

keywords = "Multiplicity of solutions, Nonlinear Dirichlet problem",

author = "Alfonso Castro and Jorge Cossio and Neuberger, {John M.}",

year = "1997",

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T1 - On multiple solutions of a nonlinear Dirichlet problem

AU - Castro, Alfonso

AU - Cossio, Jorge

AU - Neuberger, John M.

PY - 1997/12

Y1 - 1997/12

N2 - We prove that a semilinear elliptic boundary value problem has five solutions when the range of the derivative of the nonlinearity includes at least the first two eigenvalues. We also prove that if the region is a ball the semilinear elliptic problem has two solutions that change sign and are nonradial.

AB - We prove that a semilinear elliptic boundary value problem has five solutions when the range of the derivative of the nonlinearity includes at least the first two eigenvalues. We also prove that if the region is a ball the semilinear elliptic problem has two solutions that change sign and are nonradial.

KW - Multiplicity of solutions

KW - Nonlinear Dirichlet problem

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M3 - Article

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VL - 30

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JO - Nonlinear Analysis, Theory, Methods and Applications

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