Multiple solutions to nonlinear Schrödinger equations with critical growth
1 Department of Mathematics, Jiangxi University of Science and Technology, Ganzhou, 341000, P.R. China
2 School of Mathematics and Statistics, Lanzhou University, Lanzhou, 730000, P.R. China
Boundary Value Problems 2013, 2013:199 doi:10.1186/1687-2770-2013-199Published: 4 September 2013
In 2000, Cingolani and Lazzo (J. Differ. Equ. 160:118-138, 2000) studied nonlinear Schrödinger equations with competing potential functions and considered only the subcritical growth. They related the number of solutions with the topology of the global minima set of a suitable ground energy function. In the present paper, we establish these results in the critical case. In particular, we remove the condition , which is a key condition in their paper. In the proofs we apply variational methods and Ljusternik-Schnirelmann theory.
MSC: 35J60, 35Q55.