NON-NEHARI MANIFOLD METHOD FOR SUPERLINEAR SCHRODINGER EQUATION

We consider the boundary value problem (0.1) {-Delta u + V(x)u = f(x, u), x is an element of Omega, u = 0, x is an element of partial derivative Omega, where Omega subset of R-N is a bounded domain, inf(Omega) V (x) > -infinity, f is a superlinear, subcritical nonlinearity. Inspired by previous work of Szulkin and Weth (2009) [21] and (2010) [22], we develop a more direct and simpler approach on the basis of one used in [21], to deduce weaker conditions under which problem (0.1) has a ground state solution of Nehari-Pankov type or infinity many nontrivial solutions. 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.