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Multiple solutions to the nonhomogeneous [formula omitted]-Kirchhoff elliptic equation with concave–convex nonlinearities

Authors
Journal
Applied Mathematics Letters
0893-9659
Publisher
Elsevier
Volume
26
Issue
7
Identifiers
DOI: 10.1016/j.aml.2013.02.011
Keywords
  • [Formula Omitted]-Kirchhoff Elliptic Equation
  • Mountain Pass Theorem
  • Ekeland’S Variational Principle
  • Multiple Solutions

Abstract

Abstract In this paper, we study the multiplicity of solutions for the nonhomogeneous p-Kirchhoff elliptic equation (0.1) −M(‖∇u‖pp)Δpu=λh1(x)|u|q−2u+h2(x)|u|r−2u+h3(x),x∈Ω, with zero Dirichlet boundary condition on ∂Ω, where Ω is the complement of a smooth bounded domain D in RN(N≥3). λ>0, M(s)=a+bsk,a,b>0,k≥0, h1(x),h2(x) and h3(x) are continuous functions which may change sign on Ω. The parameters p,q,r satisfy 1<q<p(k+1)<r<p∗=NpN−p. A new existence result for multiple solutions is obtained by the Mountain Pass Theorem and Ekeland’s variational principle.

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