Least energy solutions for a quasilinear Schrödinger equation with potential well
College of Mathematics and Computer Science, Northwest University for Nationalities, Lanzhou, 730124, P.R. China
College of Mathematics and Statistics, Northwest Normal University, Lanzhou, 730070, P.R. China
Boundary Value Problems 2013, 2013:9 doi:10.1186/1687-2770-2013-9Published: 21 January 2013
In this paper, we consider the existence of least energy solutions for the following quasilinear Schrödinger equation:
with having a potential well, where and is a parameter. Under suitable hypotheses, we obtain the existence of a least energy solution of () which localizes near the potential well for λ large enough by using the variational method and the concentration compactness method in an Orlicz space.
MSC: 35J60, 35B33.