Non-Nehari Manifold Method for Periodic Discrete Superlinear Schr(o|¨)dinger Equation

We consider the nonlinear difference equations of the form Lu=f(n,u),n∈Z,where L is a Jacobi operator given by(Lu)(n)=a(n)u(n+1)+a(n-1)u(n-1)+b(n)u(n) for n ∈Z,{a(n)} and {b(n)} are real valued N-periodic sequences,and f(n,t) is superlinear on t.Inspired by previous work of Pankov[Discrete Contin.Dyn.Syst.,19,419-430(2007)]and Szulkin and Weth[J.Funct.Anal.,257,3802-3822(2009)],we develop a non-Nehari manifold method to find ground state solutions of Nehari-Pankov type under weaker conditions on f.Unlike the Nehari manifold method,the main idea of our approach lies on finding a minimizing Cerami sequence for the energy functional outside the Nehari-Pankov manifold by using the diagonal method.