MULTIPLICITY AND CONCENTRATION OF SOLUTIONS TO A FRACTIONAL $\frac{N}{S}$-LAPLACIAN PROBLEM WITH EXPONENTIAL CRITICAL GROWTH AND POTENTIALS COMPETITION

  • Wei CHEN ,
  • Chao JI ,
  • Nguyen Van THIN
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  • 1. Chongqing University of Posts and Telecommunications, School of Science, Chongqing 400065, China;
    2. School of Mathematics, East China University of Science and Technology, Shanghai 200237, China;
    3. Department of Mathematics, Thai Nguyen University of Education, Luong Ngoc Quyen street, Thai Nguyen city, Thai Nguyen, Viet Nam; Thang Long Institute of Mathematics and Applied Sciences, Thang Long University, Nghiem Xuan Yem, Hoang Mai, Hanoi, Viet Nam
Wei CHEN, E-mail: weichensdu@126.com; Chao JI, E-mail: jichao@ecust.edu.cn

Received date: 2023-09-25

  Revised date: 2024-05-23

  Online published: 2025-09-30

Supported by

National Natural Science Foundation of China (No. 12171152). The third author was supported by Thang Long University under project with the name "Nevanlinna theory and Kirchhoff-Schrödinger-Hardy type problems for the fractional p-Laplacian" and grant number: 01/2020/STS01.

Abstract

By using the Ljusternik-Schnirelmann category and variational method, we study the existence, multiplicity and concentration of solutions to the fractional Schrödinger equation with potentials competition as follows, $$ \varepsilon^{N}(-\Delta)_{N/s}^{s}u+V(x)|u|^{\frac{N}{s}-2}u=Q(x)h(u)\,\,in\,\, \mathbb R^{N},$$ where $\varepsilon>0$ is a parameter, $s\in (0,1)$, $2\le p<+\infty$ and $N=ps$. The nonlinear term $h$ is a differentiable function with exponential critical growth, the absorption potential $V$ and the reaction potential $Q$ are continuous functions.

Cite this article

Wei CHEN , Chao JI , Nguyen Van THIN . MULTIPLICITY AND CONCENTRATION OF SOLUTIONS TO A FRACTIONAL $\frac{N}{S}$-LAPLACIAN PROBLEM WITH EXPONENTIAL CRITICAL GROWTH AND POTENTIALS COMPETITION[J]. Acta mathematica scientia, Series B, 2025 , 45(3) : 885 -918 . DOI: 10.1007/s10473-025-0309-1

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