Solutions to a nonlinear Schrödinger equation with periodic potential and zero on the boundary of the spectrum

Jarosław Mederski
2015 Topological Methods in Nonlinear Analysis  
We study the following nonlinear Schrödinger equation where V : R N → R and g : R N ×R → R are periodic in x. We assume that 0 is a right boundary point of the essential spectrum of −∆ + V . The superlinear and subcritical term g satisfies a Nehari type monotonicity condition. We employ a Nehari manifold type technique in a strongly indefitnite setting and obtain the existence of a ground state solution. Moreover, we get infinitely many geometrically distinct solutions provided that g is odd.
doi:10.12775/tmna.2015.067 fatcat:wlrltohypvf7ngtdzjs2rnelgu