A fibering map approach to a semilinear elliptic boundary value problem

Kenneth J. Brown, Tsung Fang Wu

Research output: Contribution to journalArticle

Abstract

We prove the existence of at least two positive solutions for the semilinear elliptic boundary-value problem - ?u(x) = ?a(x)u q + b(x)up for x ?O; u(x) = 0 for x ? ?O on a bounded region O by using the Nehari manifold and the fibering maps associated with the Euler functional for the problem. We show how knowledge of the fibering maps for the problem leads to very easy existence proofs. © 2007 Texas State University.

Original languageEnglish
Pages (from-to)1-9
Number of pages9
JournalElectronic Journal of Differential Equations
Volume2007
Publication statusPublished - 10 May 2007

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Semilinear Elliptic Boundary Value Problem
Nehari Manifold
Euler
Positive Solution
Knowledge

Keywords

  • Fibering map
  • Nehari manifold
  • Semilinear elliptic boundary value problem
  • Variational methods

Cite this

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abstract = "We prove the existence of at least two positive solutions for the semilinear elliptic boundary-value problem - ?u(x) = ?a(x)u q + b(x)up for x ?O; u(x) = 0 for x ? ?O on a bounded region O by using the Nehari manifold and the fibering maps associated with the Euler functional for the problem. We show how knowledge of the fibering maps for the problem leads to very easy existence proofs. {\circledC} 2007 Texas State University.",
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A fibering map approach to a semilinear elliptic boundary value problem. / Brown, Kenneth J.; Wu, Tsung Fang.

In: Electronic Journal of Differential Equations, Vol. 2007, 10.05.2007, p. 1-9.

Research output: Contribution to journalArticle

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AU - Wu, Tsung Fang

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N2 - We prove the existence of at least two positive solutions for the semilinear elliptic boundary-value problem - ?u(x) = ?a(x)u q + b(x)up for x ?O; u(x) = 0 for x ? ?O on a bounded region O by using the Nehari manifold and the fibering maps associated with the Euler functional for the problem. We show how knowledge of the fibering maps for the problem leads to very easy existence proofs. © 2007 Texas State University.

AB - We prove the existence of at least two positive solutions for the semilinear elliptic boundary-value problem - ?u(x) = ?a(x)u q + b(x)up for x ?O; u(x) = 0 for x ? ?O on a bounded region O by using the Nehari manifold and the fibering maps associated with the Euler functional for the problem. We show how knowledge of the fibering maps for the problem leads to very easy existence proofs. © 2007 Texas State University.

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