Existence of solutions to asymptotically periodic Schrödinger equations
Date
2017-01-13
Authors
Furtado, Marcelo
de Marchi, Reinaldo
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
We show the existence of a nonzero solution for the semilinear Schrödinger equation -∆u + V(x)u = ƒ(x, u). The potential V is periodic and 0 belongs to a gap of σ(-∆ + V). The function ƒ is superlinear and asymptotically periodic with respect to x variable. In the proof we apply a new critical point theorem for strongly indefinite functionals proved in [3].
Description
Keywords
Strongly indefinite functionals, Schrödinger equation, Asymptotically periodic problem
Citation
Furtado, M. F., & Marchi, R. (2017). Existence of solutions to asymptotically periodic Schrödinger equations. <i>Electronic Journal of Differential Equations, 2017</i>(15), pp. 1-7.
Rights
Attribution 4.0 International