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

Abstract

We consider the fourth-order problem {ε4△2u + V(x)u = f(u) +γ |U|2..-2u inRN u ∈ H 2(RN), where ε > 0, N ≥ 5, V is a positive continuous potential, is a function with subcritical growth and γ ∈ {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 γ = 0 and the critical case γ = 1. In the proofs we apply Ljusternik-Schnirelmann theory.