Non-Nehari Manifold Method for Periodic Discrete Superlinear Schrodinger Equation

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 is an element of 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.