Existence and multiplicity of solutions for an elliptic system with nonlinear boundary conditions Original Research Article

In this paper we prove the existence and multiplicity of solutions for the elliptic system View the MathML sourceΔu=u,Δv=vinΩ Turn MathJax on with nonlinear coupling at the smooth boundary given by View the MathML source∂u∂ν=Hu,∂v∂ν=Hvon∂Ω, Turn MathJax on where ΩΩ is a bounded domain of RNRN with smooth boundary, ∂/∂ν∂/∂ν is the outer normal derivative. The proofs are done under suitable assumptions on the Hamiltonian, and based on the local linking theorem and a multiple critical points theorem of the critical point theory.