POSITIVE SOLUTIONS WITH HIGH ENERGY FOR FRACTIONAL SCHRÖDINGER EQUATIONS*

  • Qing Guo ,
  • Leiga Zhao
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  • 1. College of Science, Minzu University of China, Beijing 100081, China;
    2. School of Mathematics and Statistics, Beijing Technology and Business University, Beijing 100048, China
Qing Guo, E-mail: guoqing0117@163.com

Received date: 2021-05-24

  Revised date: 2022-08-22

  Online published: 2023-06-06

Supported by

NNSF of China (12171014, 12271539, 12171326), the Beijing Municipal Commission of Education (KZ202010028048) and the Research Foundation for Advanced Talents of Beijing Technology and Business University (19008022326).

Abstract

In this paper, we study the Schrödinger equations
$ (-\Delta)^s u+ V(x)u= a(x)|u|^{p-2}u+b(x)|u|^{q-2}u,\ \ x\in\ {\mathbb{R}}^{N},$
where $0<s<1$, $2<q<p<2^*_s$, $2^*_s$ is the fractional Sobolev critical exponent. Under suitable assumptions on $V$, $a$ and $b$ for which there may be no ground state solution, the existence of positive solutions are obtained via variational methods.

Cite this article

Qing Guo , Leiga Zhao . POSITIVE SOLUTIONS WITH HIGH ENERGY FOR FRACTIONAL SCHRÖDINGER EQUATIONS*[J]. Acta mathematica scientia, Series B, 2023 , 43(3) : 1116 -1130 . DOI: 10.1007/s10473-023-0308-z

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