Electron. J. Differential Equations, Vol. 2017 (2017), No. 38, pp. 1-9.

Multiplicity of ground state solutions for discrete nonlinear Schrodinger equations with unbounded potentials

Xia Liu, Tao Zhou, Haiping Shi

The discrete nonlinear Schrodinger equation is a nonlinear lattice system that appears in many areas of physics such as nonlinear optics, biomolecular chains and Bose-Einstein condensates. In this article, we consider a class of discrete nonlinear Schrodinger equations with unbounded potentials. We obtain some new sufficient conditions on the multiplicity results of ground state solutions for the equations by using the symmetric mountain pass lemma. Recent results in the literature are greatly improved.

Submitted September 8, 2016. Published February 2, 2017.
Math Subject Classifications: 39A12, 39A70, 35C08.
Key Words: Ground state solutions; critical point theory; discrete nonlinear Schrodinger equation.

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Xia Liu
Oriental Science and Technology College
Hunan Agricultural University
Changsha 410128, China.
email: xia991002@163.com
Tao Zhou
School of Business Administration
South China University of Technology
Guangzhou 510640, China
email: zhoutaoscut@hotmail.com
Haiping Shi
Modern Business and Management Department
Guangdong Construction Polytechnic
Guangzhou 510440, China
email: shp7971@163.com

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