Weighted Sobolev spaces and ground state solutions for quasilinear elliptic problems with unbounded and decaying potentials
College of Sciences, University of Shanghai for Science and Technology, Shanghai, 200093, P.R. China
Boundary Value Problems 2013, 2013:189 doi:10.1186/1687-2770-2013-189Published: 23 August 2013
In this paper, we prove some continuous and compact embedding theorems for weighted Sobolev spaces, and consider both a general framework and spaces of radially symmetric functions. In particular, we obtain some a priori Strauss-type decay estimates. Based on these embedding results, we prove the existence of ground state solutions for a class of quasilinear elliptic problems with potentials unbounded, decaying and vanishing.
MSC: 35J20, 35J60, 35Q55.