On a nonlinear elliptic system with symmetric coupling

Multiplicity results are proved for the nonlinear elliptic system in a bounded domain in R^n with smooth boundary and a nonlinear nonlinear C^1-function g which satisfies additional conditions. No assumption of symmetry on g 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.