Soliton solutions for quasilinear Schrodinger equations with critical growth

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:248

Article

Bezerra do O, Joao M.²  Miyagaki, Olimpio H.¹  Soares, Sergio H. M.³ 

[1] Univ Fed Vicosa, Dept Matemat, BR-36571000 Vicosa, MG, Brazil

[2] Univ Fed Paraiba, Dept Matemat, BR-58059900 Joao Pessoa, PB, Brazil

[3] Univ Sao Paulo, Dept Matemat, Inst Ciencias Matemat & Comp, BR-13560970 Sao Carlos, SP, Brazil

关键词: Schrodinger equations;    Standing wave solutions;    Variational methods;    Minimax methods;    Critical exponent;   

DOI  :  10.1016/j.jde.2009.11.030

来源: Elsevier

【 摘 要 】

In this paper we establish the existence of standing wave solutions for quasilinear Schrodinger equations involving critical growth. By using a change of variables, the quasilinear equations are reduced to semilinear one. whose associated functionals are well defined in the usual Sobolev space and satisfy the geometric conditions of the mountain pass theorem. Using this fact, we obtain a Cerami sequence converging weakly to a solution v. In the proof that v is nontrivial, the main tool is the concentration-compactness principle due to P.L. Lions together with some classical arguments used by H. Brezis and L. Nirenberg (1983) in [9]. (C) 2009 Elsevier Inc. All rights reserved.

【 授权许可】

Free