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

Abstract

We study the following nonlinear Schrödinger equation $$-\Delta u+V(x)u=g(x,u),$$ where V and g are periodic in x. We assume that 0 is a right boundary point of the essential spectrum of $-\Delta +V$. 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.

To appear in Topol. Methods Nonlinear Anal

References in corpus (1)

• Real solutions to the nonlinear Helmholtz equation with local nonlinearity

Cited by in corpus (1)

• Ground states of nonlinear Schrödinger equations with sum of periodic and inverse-square potentials