Multiplicity of nontrivial solutions to a biharmonic equation via Lusternik-Schnirelman theory

摘要

In this paper, we are concerned with the multiplicity of nontrivial solutions for the following class of biharmonic problem Δ2u=μ|u|q- 2u+|u|2-2uinΩ,u=?u?η=0on?Ω, where Ω∩RN is a bounded domain with smooth boundary. Using the Lusternik-Schnirelman theory, we relate the number of solutions with the topology of Ω.