Multiplicity of solutions for a biharmonic equation with subcritical or critical growth

Abstract

We consider the fourth-order problem{epsilon(4)Delta(2)u + V(x)u = f(u) + gamma vertical bar u vertical bar(2)**-(2)u in R-N u is an element of H-2(R-N),where epsilon > 0, N >= 5, V is a positive continuous potential, f is a function with subcritical growth and gamma is an element of {0,1}. We relate the number of solutions with the topology of the set where V attain its minimum values. We consider the subcritical case gamma = 0 and the critical case gamma = 1. In the proofs we apply Ljusternik-Schnirelmann theory.