Multiple solutions for semilinear elliptic systems with non-homogeneous boundary conditions

Abstract

Since the early seventies, many authors have widely investigated existence and multiplicity of solutions for semilinear elliptic problems with Dirichlet boundary conditions, especially by means of variational methods (see [22] and references therein). In particular, if ’ is a real L2-function on a bounded domain ⊂ Rn, p? 2 and pi 2∗ if n? 3 (here, 2∗ = 2n n−2 ), the following model problem   −6u= |u|p−2u+ ’ in ;