A Note on Nonlinear Schrödinger Equations: Unveiling the Relation Between Spectral Gaps and the Nonlinearity Behavior

Mayra Soares Costa Rodrigues, Liliane A. Maia

Published 2019-02-19Version 1

We establish the existence of a positive solution to strongly indefinite asymptotically linear and superlinear Schrodinger equations. The novelty is to identify the essential relation between the spectrum of the operator and the behavior of the nonlinear term, in order to weaken the necessary assumptions to obtain a linking structure to the problem. Our main dificulty is to overcome the lack of monotonicity on the nonlinear term, as well, as the lack of compactness since the domain is unbounded. With this purpose, we require periodicity on V .