Solutions for quasilinear Schrödinger equations with critical Sobolev-Hardyexponents

Yimin Zhang; Youjun Wang; Yaotian Shen

doi:10.3934/cpaa.2011.10.1037

Article Contents

2011, Volume 10, Issue 4: 1037-1054. Doi: 10.3934/cpaa.2011.10.1037

This issue Previous Article On the structure of solutions of nonlinear hyperbolic systems of conservation laws Next Article Nonlinear Neumann equations driven by a nonhomogeneous differential operator

Solutions for quasilinear Schrödinger equations with critical Sobolev-Hardy exponents

1.
Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, PO Box 71010, Wuhan 430071E01103
2.
Department of Mathematical Sciences, Tsinghua University, Beijing 100084e/pjp
3.
Department of Mathematics, South China University of Technology, Guangzhou 510640

Received: April 2010

Revised: September 2010

Published: July 2011

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Abstract

By using a change of variable, the quasilinear Schrödinger equation is reduced to semilinear elliptic equation. Then, Mountain Pass theorem without $(PS)_c$ condition in a suitable Orlicz space is employed to prove the existence of positive standing wave solutions for a class of quasilinear Schrödinger equations involving critical Sobolev-Hardy exponents.

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Mathematics Subject Classification: Primary: 35J20, 35J60; Secondary: 35Q55.

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