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Multiplicity theorems for a class of Dirichlet quasilinear elliptic systems involving the [formula omitted]-Laplacian

Authors
Journal
Nonlinear Analysis Theory Methods & Applications
0362-546X
Publisher
Elsevier
Publication Date
Volume
73
Issue
8
Identifiers
DOI: 10.1016/j.na.2010.06.038
Keywords
  • Three Solutions
  • Critical Point
  • [Formula Omitted]-Laplacian
  • Multiplicity Results
  • Dirichlet Problem
Disciplines
  • Mathematics

Abstract

Abstract In this paper, we prove the existence of at least three weak solutions for the quasilinear elliptic systems { Δ p 1 u 1 + λ F u 1 ( x , u 1 , u 2 , … , u n ) = 0 in Ω , Δ p 2 u 2 + λ F u 2 ( x , u 1 , u 2 , … , u n ) = 0 in Ω , … Δ p n u n + λ F u n ( x , u 1 , u 2 , … , u n ) = 0 in Ω , u i = 0 for 1 ≤ i ≤ n on ∂ Ω . Our main tool is a recent three critical points theorem of Averna and Bonanno [D. Averna, G. Bonanno, A three critical points theorem and its applications to the ordinary Dirichlet problem, Topol. Methods Nonlinear Anal. 22 (2003) 93–104].

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