PROPERTIES OF THE POSITIVE SOLUTIONS OF FRACTIONAL P&Q-LAPLACE EQUATIONS WITH A SIGN-CHANGING POTENTIAL

  • Yubo DUAN1 ,
  • Yawei WEI
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  • 1. School of Mathematical Sciences, Nankai University, Tianjin 300071, China;
    2. School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071, China
Yubo DUAN, E-mail: 1120190017@mail.nankai.edu.cn

Received date: 2023-06-07

  Revised date: 2024-07-19

  Online published: 2024-12-06

Supported by

Yawei Wei's research was partially supported by the NSFC (12271269) and the Fundamental Research Funds for the Central Universities. Yubo Duan's research was partially supported by the Fundamental Research Funds for the Central Universities (2021YJSB006).

Abstract

In this paper, we consider the nonlinear equations involving the fractional $p\&q$-Laplace operator with a sign-changing potential. This model is inspired by the De Giorgi Conjecture. There are two main results in this paper. First, in the bounded domain, we use the moving plane method to show that the solution is radially symmetric. Second, for the unbounded domain, in view of the idea of the sliding method, we find the existence of the maximizing sequence of the bounded solution, then obtain that the solution is strictly monotone increasing in some direction.

Cite this article

Yubo DUAN1 , Yawei WEI . PROPERTIES OF THE POSITIVE SOLUTIONS OF FRACTIONAL P&Q-LAPLACE EQUATIONS WITH A SIGN-CHANGING POTENTIAL[J]. Acta mathematica scientia, Series B, 2024 , 44(6) : 2422 -2442 . DOI: 10.1007/s10473-024-0620-2

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