Non Nehari manifold method for periodic discrete superlinear Schrodinger equation
We consider the nonlinear difference equations of the form $Lu f\left( {n,u} \right);n \in 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.