The existence of solutions for superquadratic Hamiltonian elliptic systems on R

This paper is concerned with the following Hamiltonian elliptic system: View the MathML source{−△u+V(x)u=Hu(x,u,v)in RN;−△v+V(x)v=−Hv(x,u,v)in RN;u(x)→0andv(x)→0as |x|→∞, Turn MathJax on where V(x)∈C(RN,R)V(x)∈C(RN,R) and H(x,z)H(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 obtain infinitely many solutions for the above system.