# American Institute of Mathematical Sciences

July  2011, 10(4): 1037-1054. doi: 10.3934/cpaa.2011.10.1037

## 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, China 2 Department of Mathematical Sciences, Tsinghua University, Beijing 100084e/pjp, China 3 Department of Mathematics, South China University of Technology, Guangzhou 510640, China

Received  April 2010 Revised  September 2010 Published  April 2011

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.
Citation: Yimin Zhang, Youjun Wang, Yaotian Shen. Solutions for quasilinear Schrödinger equations with critical Sobolev-Hardy exponents. Communications on Pure & Applied Analysis, 2011, 10 (4) : 1037-1054. doi: 10.3934/cpaa.2011.10.1037
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