Existence of nontrivial solutions for asymptotically linear periodic Schrödinger equations
Shaowei Chen, Dawei Zhang · Complex Variables and Elliptic Equations · 2014
We study the Schrödinger equation:Section.Display where is periodic and is periodic in the -variables, is in a gap of the spectrum of the operator and is asymptotically linear as We prove that under some asymptotically linear assumptions for , this equation has a nontrivial solution. Our assumptions for are different from the classical assumptions raised by Li and Szulkin.