Multiplicity of solutions for p-biharmonic problems with critical growth.

Abstract

We prove the existence of infinitely many solutions for p-biharmonic problems in a bounded, smooth domain Ω with concave-convex nonlinearities dependent upon a parameter λ and a positive continuous function f:Ω¯¯¯¯→R. We simultaneously handle critical case problems with both Navier and Dirichlet boundary conditions by applying the Ljusternik-Schnirelmann method. The multiplicity of solutions is obtained when λ is small enough. In the case of Navier boundary conditions, all solutions are positive, and a regularity result is proved.