MULTIPLE SOLUTIONS FOR THE p−LAPLACE OPERATOR WITH CRITICAL GROWTH

نویسندگان

  • PABLO L. DE NÁPOLI
  • A. SILVA
چکیده

In this paper we show the existence of at least three nontrivial solutions to the following quasilinear elliptic equation −∆pu = |u| ∗ u + λf(x, u) in a smooth bounded domain Ω of R with homogeneous Dirichlet boundary conditions on ∂Ω, where p = Np/(N − p) is the critical Sobolev exponent and ∆pu = div(|∇u|∇u) is the p−laplacian. The proof is based on variational arguments and the classical concentration compactness method.

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تاریخ انتشار 2009