Acta mathematica scientia,Series B ›› 2016, Vol. 36 ›› Issue (1): 73-86.doi: 10.1016/S0252-9602(15)30079-5

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NONSMOOTH CRITICAL POINT THEOREMS AND ITS APPLICATIONS TO QUASILINEAR SCHRÖDINGER EQUATIONS

Zhouxin LI1, Yaotian SHEN2   

  1. 1. School of Mathematics and Statistics, Central South University, Changsha 400083, China;
    2. Department of Mathematics, South China University of Technology, Guangzhou 510640, China
  • Received:2014-12-05 Revised:2015-05-13 Online:2016-01-30 Published:2016-01-30
  • Supported by:

    The first author was supported by NSF of China(11201488) and Hunan Provincial Natural Science Foundation of China(14JJ4002). The second author was supported by NSF of China(11371146).

Abstract:

In this paper, the existence and nonexistence of solutions to a class of quasilinear elliptic equations with nonsmooth functionals are discussed, and the results obtained are applied to quasilinear Schrödinger equations with negative parameter which arose from the study of self-channeling of high-power ultrashort laser in matter.

Key words: nonsmooth critical point theorems, quasilinear elliptic equations, Schrödinger equation

CLC Number: 

  • 35J20
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