Abstract
In this paper we consider a class of elliptic problems of p-Kirchhoff type with critical exponent in bounded domains and new results as regards the existence and multiplicity of solutions are obtained by using the concentration-compactness principle and variational method.
Highlights
1 Introduction In this paper we deal with the existence and multiplicity of solutions to the following p-Kirchhoff type with critical exponent:
U =, x ∈ ∂, where < p < N, λ is a positive parameter, ⊂ RN is an open bounded domain with smooth boundary and λ is a positive parameter, p∗ = Np/(N – p) is the critical exponent according to the Sobolev embedding. f : × R → R, g : R+ → R+ are continuous functions that satisfy the following conditions: (G ) There exists α > such that g(t) ≥ α for all t ≥
In [ ], the author showed the existence of infinite solutions to the p-Kirchhoff-type quasilinear elliptic equation
Summary
1 Introduction In this paper we deal with the existence and multiplicity of solutions to the following p-Kirchhoff type with critical exponent: F : × R → R, g : R+ → R+ are continuous functions that satisfy the following conditions: (G ) There exists α > such that g(t) ≥ α for all t ≥ . In [ ], by means of a direct variational method, the authors proved the existence and multiplicity of solutions to a class of p-Kirchhoff-type problem with Dirichlet boundary data.
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