Electron. J. Differential Equations, Vol. 2018 (2018), No. 25, pp. 1-26.

Ground and bound states of periodic Schrodinger equations with super or asymptotically linear terms

Qingfang Wu, Dongdong Qin

This paper is concerned with existence of ground and bound states for a class of nonlinear Schrodinger equation with periodic potential. We impose general assumptions on the nonlinearity with super or asymptotically linear growth, and find some refinements of known results and new results by using the perturbation method and a mountain pass argument. In particular, a critical point theory is established for the asymptotically linear growth case.

Submitted October 4, 2017. Published January 18, 2018.
Math Subject Classifications: 35J20, 35J60, 35Q55.
Key Words: Schrodinger equations; minimax characterization; perturbation method; Nehari-Pankov manifold; ground states.

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Qingfang Wu
School of Traffic and Transportation Engineering
Central South University
Changsha, 410075 Hunan, China
email: 212032@csu.edu.cn
Dongdong Qin
School of Mathematics and Statistics
Central South University
Changsha, 410083 Hunan, China
email: qindd132@163.com

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