Multiple solutions for the p-Laplace operator with critical growth

In this paper we show the existence of at least three nontrivial solutions to the following quasilinear elliptic equation - Δp u = | u |p* - 2 u + λ f (x, u) in a smooth bounded domain Ω of RN with homogeneous Dirichlet boundary conditions on ∂ Ω, where p* = N p / (N - p) is the critical Sobolev exp...

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Detalles Bibliográficos
Autores principales: De Nápoli, P.L., Bonder, J.F., Silva, A.
Formato: JOUR
Materias:
Critical growth
p-Laplace equations
Variational methods
Bounded domain
Critical Sobolev exponent
Dirichlet boundary condition
Multiple solutions
Nontrivial solution
P-Laplace equations
P-Laplace operator
P-Laplacian
Quasilinear elliptic equations
Laplace transforms
Mathematical operators
Nonlinear equations
Laplace equation
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_0362546X_v71_n12_p6283_DeNapoli
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
Descripción
Sumario:In this paper we show the existence of at least three nontrivial solutions to the following quasilinear elliptic equation - Δp u = | u |p* - 2 u + λ f (x, u) in a smooth bounded domain Ω of RN with homogeneous Dirichlet boundary conditions on ∂ Ω, where p* = N p / (N - p) is the critical Sobolev exponent and Δp u = div (| ∇ u |p - 2 ∇ u) is the p-Laplacian. The proof is based on variational arguments and the classical concentration compactness method. © 2009 Elsevier Ltd. All rights reserved.

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