POSITIVE SOLUTIONS FOR A NONLOCAL PROBLEM WITH CRITICAL SOBOLEV EXPONENT IN HIGHER DIMENSIONS

Xiaotao Qian

doi:10.11948/20210495

2022 Volume 12 Issue 5

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Xiaotao Qian. POSITIVE SOLUTIONS FOR A NONLOCAL PROBLEM WITH CRITICAL SOBOLEV EXPONENT IN HIGHER DIMENSIONS[J]. Journal of Applied Analysis & Computation, 2022, 12(5): 2033-2042. doi: 10.11948/20210495

Citation:

Xiaotao Qian. POSITIVE SOLUTIONS FOR A NONLOCAL PROBLEM WITH CRITICAL SOBOLEV EXPONENT IN HIGHER DIMENSIONS[J]. Journal of Applied Analysis & Computation, 2022, 12(5): 2033-2042. doi: 10.11948/20210495

POSITIVE SOLUTIONS FOR A NONLOCAL PROBLEM WITH CRITICAL SOBOLEV EXPONENT IN HIGHER DIMENSIONS

Xiaotao Qian^1, ,

1.
Department of Basic Teaching and Research, Yango University, Fuzhou, 350015, China

Corresponding author: Email: qianxiaotao1984@163.com(X. Qian)
Fund Project: The author was supported by National Natural Science Foundation of China (No. 11871152) and Natural Science Foundation of Fujian Province (No. 2021J01330)

Abstract

Abstract

This paper is devoted to a nonlocal problem involving critical Sobolev exponent and negative nonlocal term. By virtue of a cut-off technique and the concentration compactness principle, we prove the existence and asymptotic behavior of positive solutions for the considered problem. In particular, our results generalize the existence results of positive solutions to higher dimensions $N\ge 5$.
- Variational methods /
- nonlocal problem /
- positive solution /
- critical Sobolev exponent
MSC: 35J20, 35J60

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References

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