Research
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:10.1186/1687-2770-2013-9
Published: 21 January 2013Abstract
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.
