On a nonlinear elliptic system with symmetric coupling

Multiplicity results are proved for the nonlinear elliptic system {−Δu+g(v)=0−Δv+g(u)=0in Ω,u=v=0on ∂Ω, where Ω⊂RNΩ⊂RN is a bounded domain with smooth boundary and g:R⟶Rg:R⟶R is a nonlinear C1C1-function which satisfies additional conditions. No assumption of symmetry on gg is imposed.Extensive use is made of a global version of the Lyapunov–Schmidt reduction method due to Castro and Lazer and of symmetric versions of the Mountain Pass Theorem.