Localized nodal solutions for quasilinear Schrodinger equations

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:267

Article

Liu, Xiangqing¹  Liu, Jiaquan²  Wang, Zhi-Qiang^3,4 

[1] Yunnan Normal Univ, Dept Math, Kunming 650500, Yunnan, Peoples R China

[2] Peking Univ, Sch Math Sci, LMAM, Beijing 100871, Peoples R China

[3] Fujian Normal Univ, Coll Math & Informat, FJKLMAA, Fuzhou 350117, Fujian, Peoples R China

[4] Utah State Univ, Dept Math & Stat, Logan, UT 84322 USA

关键词: Modified nonlinear Schrodinger equation (MNLS);    Variational perturbation method;    Semiclassical states;    Nodal solutions;   

DOI  :  10.1016/j.jde.2019.08.003

来源: Elsevier

【 摘 要 】

In this paper, we study the existence of localized nodal solutions for a class of semiclassical quasilinear Schrodinger equations including, as a special case, the Modified Nonlinear Schrodinger Equation (MNLS) epsilon(2)(Delta nu + 1/2 nu Delta nu(2)) - V (x) nu + vertical bar nu vertical bar(q-2)nu =0, in R-N , nu(x) -> 0 as vertical bar x vertical bar -> infinity. We establish for small epsilon the existence of a sequence of localized nodal solutions concentrating near a given local minimum point of the potential function, by developing new variational perturbation method to treat this class of non-smooth variational problems. The new method allows the perturbed variational functionals to share critical points with the original functional. This method allows us to avoid any limiting process from the perturbed problems to the original problem, and it is effective in dealing with multiple existence of solutions. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

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