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Open Access Research

Weighted Sobolev spaces and ground state solutions for quasilinear elliptic problems with unbounded and decaying potentials

Guoqing Zhang

Author Affiliations

College of Sciences, University of Shanghai for Science and Technology, Shanghai, 200093, P.R. China

Boundary Value Problems 2013, 2013:189  doi:10.1186/1687-2770-2013-189

Published: 23 August 2013

Abstract

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.

Keywords:
weighted Sobolev spaces; unbounded and decaying potentials; quasilinear elliptic problems