SUPER-CRITICAL PROBLEMS INVOLVING THE FRACTIONAL $P$-LAPLACIAN

Zijian Wu; Haibo Chen

doi:10.11948/20220353

2023 Volume 13 Issue 4

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Zijian Wu, Haibo Chen. SUPER-CRITICAL PROBLEMS INVOLVING THE FRACTIONAL $P$-LAPLACIAN[J]. Journal of Applied Analysis & Computation, 2023, 13(4): 2065-2073. doi: 10.11948/20220353

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Zijian Wu, Haibo Chen. SUPER-CRITICAL PROBLEMS INVOLVING THE FRACTIONAL $P$-LAPLACIAN[J]. Journal of Applied Analysis & Computation, 2023, 13(4): 2065-2073. doi: 10.11948/20220353

SUPER-CRITICAL PROBLEMS INVOLVING THE FRACTIONAL $P$-LAPLACIAN

Zijian Wu^1,,
Haibo Chen^1, ,

1.
School of Mathematics and Statistics, Central South University, Yuelu Street, 410083 Changsha, China

Author Bio: Email: wuzijian_math@163.com(Z. Wu)
Corresponding author: Email: math_chb@csu.edu.cn(H. Chen)

Abstract

Abstract

This paper is concerned with the following non-local problems
$ \begin{equation*} (-\Delta)_p^su+V(x)|u|^{p-2}u=w+h(u), \mbox{ in } \mathbb{R}^2, \end{equation*} $
where $ 0<s<1<p<\infty $, $ sp<2 $ and $ 0<w\in L^\infty( \mathbb{R}^2) $. Here the nonlinearity $ h $ imposes no growth restriction. By new variational principles, a nontrivial solution to this problem is obtained. This result is new because of the super-critical nonlinearity $ h $.
- Super-critical /
- fractional p-Laplacian /
- variational principle
MSC: 35J60, 35J66

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References

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