AN ASYMPTOTICALLY PERIODIC SCHRÖDINGER EQUATION WITH INDEFINITE LINEAR PART
Gongbao Li, Andrzej Szulkin · Communications in Contemporary Mathematics · 2002
We consider the Schrödinger equation - Δ u + V(x)u = f(x,u), where V is periodic and f asymptotically periodic in the x-variables, 0 is in a spectral gap of - Δ + V and f is either asymptotically linear or superlinear as |u| → ∞. We show that this equation has a solution u ∈ H1(RN), u ≠ 0.