Existence of Nontrivial Solutions for Periodic Schrödinger Equations with New Nonlinearities - Shaowei Chen; Dawei Zhang (Abstract and Applied Analysis)
We study the Schrödinger equation: -Δu+Vxu+fx,u=0,  u∈H1(RN), where V is 1-periodic and f is 1-periodic in the x-variables; 0 is in a gap of the spectrum of the operator -Δ+V. We prove that, under some new assumptions for f, this equation has a nontrivial solution. Our assumptions for the nonlinearity f are very weak and greatly different from the known assumptions in the literature.