Título :	A note on nonlinear Schrödinger equations : the relation between spectral gaps and the nonlinearity
Autor :	Maia, Liliane de Almeida Rodrigues, Mayra Soares Costa
Assunto::	Schrödinger, Equação de Métodos variacionais Teoria espectral
Fecha de publicación :	2020
Editorial :	Elsevier
Citación :	MAIA, Liliane de A.; SOARES, Mayra. A note on nonlinear Schrödinger equations: the relation between spectral gaps and the nonlinearity. Journal of Mathematical Analysis and Applications, v. 492, n. 2, 124509, 15 dez. 2020. DOI: https://doi.org/10.1016/j.jmaa.2020.124509.
Abstract:	We establish the existence of a nontrivial weak solution to strongly indefinite asymptotically linear and superlinear Schrödinger equations. The novelty is to identify the essential relation between the spectrum of the operator and the behavior of the nonlinear term. Our goal is to weaken the necessary assumptions to obtain a linking structure to the problem, for instance to allow zero being in the spectrum or the nonlinearity being sign-changing. Our main difficulty 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.
DOI:	https://doi.org/10.1016/j.jmaa.2020.124509
metadata.dc.relation.publisherversion:	https://www.sciencedirect.com/science/article/abs/pii/S0022247X20306715#!
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