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Nontrivial solutions of a class of nonlocal problems via local linking theory

Authors
Journal
Applied Mathematics Letters
0893-9659
Publisher
Elsevier
Publication Date
Volume
23
Issue
4
Identifiers
DOI: 10.1016/j.aml.2009.11.001
Keywords
  • Nonlocal Problems
  • Kirchhoff’S Equation
  • Local Linking

Abstract

Abstract The existence of nontrivial solutions of Kirchhoff type equations is an important nonlocal quasilinear problem. In this paper, by using the local linking theory, we obtain nontrivial solutions of a class of nonlocal quasilinear elliptic boundary value problems as follows: { − ( a + b ∫ Ω | ∇ u | 2 ) Δ u = f ( x , u ) , in Ω ; u = 0 , on ∂ Ω .

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