On ground state for a class of nonlinear Schrödinger equation

I study the existence of ground state for the following periodic Schrödinger equation under the circumstance that the nonlinear term satisfies odd conditions by using the Mountain Pass Lemma and variational method. $$-\Delta u+V(x)u-\Delta(1+u^2)^{{1}/{2}}{u\over 2(1+u^2)^{{1}/{2}}}=f\,(x, u).$$

Bibliographic Details
Main Author: Ahamed Adam Abdelgadir
Format: Article
Language:English
Published: Taylor & Francis Group 2018-03-01
Series:Journal of Taibah University for Science
Subjects:
Online Access:http://dx.doi.org/10.1080/16583655.2018.1451058
Description
Summary:I study the existence of ground state for the following periodic Schrödinger equation under the circumstance that the nonlinear term satisfies odd conditions by using the Mountain Pass Lemma and variational method. $$-\Delta u+V(x)u-\Delta(1+u^2)^{{1}/{2}}{u\over 2(1+u^2)^{{1}/{2}}}=f\,(x, u).$$
ISSN:1658-3655