EXISTENCE AND MULTIPLICITY OF SOLUTIONS FOR $P(X)$-LAPLACIAN DIFFERENTIAL INCLUSIONS INVOLVING CRITICAL GROWTH

Ziqing Yuan; Mugen Huang

doi:10.11948/20190216

2020 Volume 10 Issue 4

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Ziqing Yuan, Mugen Huang. EXISTENCE AND MULTIPLICITY OF SOLUTIONS FOR $P(X)$-LAPLACIAN DIFFERENTIAL INCLUSIONS INVOLVING CRITICAL GROWTH[J]. Journal of Applied Analysis & Computation, 2020, 10(4): 1416-1432. doi: 10.11948/20190216

Citation:

Ziqing Yuan, Mugen Huang. EXISTENCE AND MULTIPLICITY OF SOLUTIONS FOR $P(X)$-LAPLACIAN DIFFERENTIAL INCLUSIONS INVOLVING CRITICAL GROWTH[J]. Journal of Applied Analysis & Computation, 2020, 10(4): 1416-1432. doi: 10.11948/20190216

EXISTENCE AND MULTIPLICITY OF SOLUTIONS FOR $P(X)$-LAPLACIAN DIFFERENTIAL INCLUSIONS INVOLVING CRITICAL GROWTH

Ziqing Yuan^1,3, ,,
Mugen Huang^2, ,

1.
Department of Mathematics, Shaoyang University, Shaoyang, Hunan, 422000, China
2.
School of Statistics and Mathematics, Big Data and Educational Statistics Application Laboratory, Guangdong University of Finance and Economics, Guangzhou, 510320, China
3.
Center for Applied Mathematics, Guangzhou University, Guangzhou, Guangdong, 510006, China

Corresponding authors: Email address: junjyuan@sina.com(Z. Yuan); Email address: mghuang@gdufe.edu.cn(M. Huang)
Fund Project: The authors were supported by the Hunan Province Natural Science Foundation of China (Grant No. 2017JJ3222), the National Natural Science Foundation of China (Grant No.11901126), the Natural Science Foundation of Guangdong Province(2017A030310597), and the Scientific Research fund of Hunan provincial Education Department (18C0809)

Abstract

Abstract

This paper concernes with the existence and multiplicity of solutions for $p(x)$-Laplacian differential inclusions involving critical growth. The main tools are the nonsmooth analysis and variational methods. Our main results generalize some recent results in the literature into nonsmooth cases.
- Locally Lipschitz /
- nonsmooth analysis /
- hemivariational inequality
MSC: 35R70, 35J70, 49J52

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References

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