Positive, negative, and sign-changing solutions to a quasilinear Schrodinger equation with a parameter

被引：7

作者：

Yang, Xianyong ^{[1
,2
]}

Tang, Xianhua ^{[1
]}

Zhang, Youpei ^{[1
]}

机构：

[1] Cent S Univ, Sch Math & Stat, Changsha 410205, Hunan, Peoples R China

[2] Yunnan Minzu Univ, Sch Preparatory Educ, Kunming 650500, Yunnan, Peoples R China

来源：

JOURNAL OF MATHEMATICAL PHYSICS | 2019年 / 60卷 / 12期

关键词：

SOLITON-SOLUTIONS; NONRADIAL SOLUTIONS; ELLIPTIC-EQUATIONS; WAVE SOLUTIONS; EXISTENCE;

D O I：

10.1063/1.5116602

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

In this paper, we study the following quasilinear Schrodinger equation with a parameter: -Delta u + V(x)u - kappa alpha Delta(vertical bar u vertical bar(2 alpha))vertical bar u vertical bar(2 alpha-2)u = vertical bar u vertical bar(p-2)u + vertical bar u vertical bar((2 alpha)2)*(-2)u in R-N, where N >= 3, alpha > 1/2, 2 < p < (2 alpha)2*, and kappa is a positive constant. Under different assumptions on V, we obtain the existence of positive, negative, and sign-changing solutions. Our results generalize the results of Liu et al. [J. Differ. Equations 187, 473-493 (2003)] into the critical case for general alpha. Published under license by AIP Publishing.

引用

页数：24

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