Existence of solutions for nonperiodic superquadratic Hamiltonian elliptic systems Original Research Article

This paper is concerned with the following nonperiodic Hamiltonian elliptic system View the MathML source{−Δu+V(x)u=Rv(x,u,v)in RN,−Δv+V(x)v=Ru(x,u,v)in RN,u(x)→0andv(x)→0as |x|→∞, Turn MathJax on where R(x,z)R(x,z) is superquadratic in zz as |z|→∞|z|→∞ with z=(u,v)z=(u,v). By applying a critical point theorem for strongly indefinite functionals, we prove the existence of solution for the above system.