Existence of solutions for fourth order elliptic equations of Kirchhoff type

Fanglei Wang, Mustafa Avci, Yukun An

Research output: Contribution to journalJournal Articlepeer-review

70 Citations (Scopus)

Abstract

This paper is concerned with the existence of nontrivial solutions for a class of fourth order elliptic equations of Kirchhoff type (1){δ2u-λ(a+b∫Ω|∇;u|2dx)δu=f(x,u),inΩ,u=0,δu=0,on∂Ω, where a>0, b≥0 are constants, and λ>0 is a parameter. We will show that there exists a λ* such that (1) has nontrivial solutions for 0<λ<λ* by using the mountain pass techniques and the truncation method.

Original languageEnglish
Pages (from-to)140-146
Number of pages7
JournalJournal of Mathematical Analysis and Applications
Volume409
Issue number1
DOIs
Publication statusPublished - 1 Jan. 2014

Keywords

  • Fourth order elliptic equation
  • Mountain pass theorem
  • Nontrivial solutions
  • Truncation method

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