数学物理学报(英文版) ›› 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

李周欣1, 沈尧天2   

  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
  • 收稿日期:2014-12-05 修回日期:2015-05-13 出版日期:2016-01-30 发布日期:2016-01-30
  • 作者简介:Zhouxin LI,E-mail:lzx@math.pku.edu.cn;Yaotian SHEN,E-mail:maytshen@scut.edu.cn
  • 基金资助:

    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).

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).

摘要:

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.

关键词: nonsmooth critical point theorems, quasilinear elliptic equations, Schrödinger equation

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

中图分类号: 

  • 35J20