Multiplicity Result for a Degenerate Elliptic Equation with Logistic Reaction

Research output: Contribution to journalArticle

42 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)138-144
Number of pages7
JournalJournal of Differential Equations
Volume173
Issue number1
DOIs
Publication statusPublished - 2001 Jun 10
Externally publishedYes

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Boundary conditions

Keywords

  • Degenerate elliptic equation
  • Mountain pass theorem
  • Multiple solutions
  • P-Laplace operator

ASJC Scopus subject areas

  • Analysis

Cite this

Multiplicity Result for a Degenerate Elliptic Equation with Logistic Reaction. / Takeuchi, Shingo.

In: Journal of Differential Equations, Vol. 173, No. 1, 10.06.2001, p. 138-144.

Research output: Contribution to journalArticle

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