EXISTENCE AND CONCENTRATION OF SOLUTIONS FOR DISCONTINUOUS ELLIPTIC PROBLEMS WITH CRITICAL GROWTH

Ziqing Yuan

doi:10.11948/20240241

2025 Volume 15 Issue 2

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Ziqing Yuan. EXISTENCE AND CONCENTRATION OF SOLUTIONS FOR DISCONTINUOUS ELLIPTIC PROBLEMS WITH CRITICAL GROWTH[J]. Journal of Applied Analysis & Computation, 2025, 15(2): 973-992. doi: 10.11948/20240241

Citation:

Ziqing Yuan. EXISTENCE AND CONCENTRATION OF SOLUTIONS FOR DISCONTINUOUS ELLIPTIC PROBLEMS WITH CRITICAL GROWTH[J]. Journal of Applied Analysis & Computation, 2025, 15(2): 973-992. doi: 10.11948/20240241

EXISTENCE AND CONCENTRATION OF SOLUTIONS FOR DISCONTINUOUS ELLIPTIC PROBLEMS WITH CRITICAL GROWTH

Ziqing Yuan^,

Department of Mathematics, Shaoyang University, Shaoyang, Hunan 422000, China

Corresponding author: Email: junjyuan@sina.com(Z. Yuan)
Fund Project: The author was supported by the Natural Science Foundation of Hunan Provincial (Grant No. 2023JJ30559) and the National Natural Science Foundation of China (Grant No. 11901126)

Abstract

Abstract

This paper concerns the following elliptical problem with discontinuous nonlinearity
$\left\{\begin{array}{l}-\epsilon^2 \Delta u+V(x) u=f(u)+|u|^{2^*-2} u, \quad x \in \mathbb{R}^N, \\u>0,\end{array}\right.$
where N ≥ 3, ε > 0 and f(u) is a discontinuous function. We obtain the existence and concentration results of this problem. Our results generalize some recent results on this kind of problems. In order to obtain these results, a suitable truncation, concentration compactness principle, new analytic technique and variational method are used.
- Elliptic problem /
- concentration /
- variational method /
- discontinuous nonlinearity
MSC: 35Q51, 34A36, 49J52

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References

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