Multiplicity Result for a Degenerate Elliptic Equation with Logistic Reaction

研究成果: Article

42 引用 (Scopus)

抄録

A degenerate elliptic equation λΔpu+uq-1(1-ur)=0 with zero Dirichlet boundary condition, where λ is a positive parameter, 2<p<q, and r>0, is studied. It has been known that there exists a positive number Λ such that if λ>Λ, then the problem has no positive solution; if λ≤Λ, then there exists a maximal solution; and for sufficiently small λ (<Λ), the problem has at least two solutions. In this article, it is shown that if λ<Λ, then there exist at least two positive solutions, via the variational method.

元の言語English
ページ(範囲)138-144
ページ数7
ジャーナルJournal of Differential Equations
173
発行部数1
DOI
出版物ステータスPublished - 2001 6 10
外部発表Yes

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Logistics
Boundary conditions

ASJC Scopus subject areas

  • Analysis

これを引用

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abstract = "A degenerate elliptic equation λΔpu+uq-1(1-ur)=0 with zero Dirichlet boundary condition, where λ is a positive parameter, 20, is studied. It has been known that there exists a positive number Λ such that if λ>Λ, then the problem has no positive solution; if λ≤Λ, then there exists a maximal solution; and for sufficiently small λ (<Λ), the problem has at least two solutions. In this article, it is shown that if λ<Λ, then there exist at least two positive solutions, via the variational method.",
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AB - A degenerate elliptic equation λΔpu+uq-1(1-ur)=0 with zero Dirichlet boundary condition, where λ is a positive parameter, 20, is studied. It has been known that there exists a positive number Λ such that if λ>Λ, then the problem has no positive solution; if λ≤Λ, then there exists a maximal solution; and for sufficiently small λ (<Λ), the problem has at least two solutions. In this article, it is shown that if λ<Λ, then there exist at least two positive solutions, via the variational method.

KW - Degenerate elliptic equation

KW - Mountain pass theorem

KW - Multiple solutions

KW - P-Laplace operator

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