Kirchhoff-type differential inclusion problems involving the fractional Laplacian and strong damping

Mingqi Xiang; Binlin Zhang; Die Hu; Mingqi Xiang; Binlin Zhang; Die Hu

doi:10.3934/era.2020034

Electronic Research Archive

2020, Volume 28, Issue 2: 651-669. doi: 10.3934/era.2020034

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Kirchhoff-type differential inclusion problems involving the fractional Laplacian and strong damping

Mingqi Xiang ^{1
,},
Binlin Zhang ^{2
,
,},
Die Hu ^{1
,}

1.
College of Science, Civil Aviation University of China, Tianjin 300300, China
2.
College of Mathematics and System Science, Shandong University of Science and Technology, Qingdao 266590, China

Received: 01 December 2019 Revised: 01 March 2020
35L86, 35L70, 35L20

The aim of this paper is to investigate the existence of weak solutions for a Kirchhoff-type differential inclusion wave problem involving a discontinuous set-valued term, the fractional $ p $-Laplacian and linear strong damping term. The existence of weak solutions is obtained by using a regularization method combined with the Galerkin method.
- Fractional $ p $-Laplacian,
- Kirchhoff-type problem,
- differential inclusion,
- Galerkin approximation
Citation: Mingqi Xiang, Binlin Zhang, Die Hu. Kirchhoff-type differential inclusion problems involving the fractional Laplacian and strong damping[J]. Electronic Research Archive, 2020, 28(2): 651-669. doi: 10.3934/era.2020034

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Abstract

The aim of this paper is to investigate the existence of weak solutions for a Kirchhoff-type differential inclusion wave problem involving a discontinuous set-valued term, the fractional $ p $-Laplacian and linear strong damping term. The existence of weak solutions is obtained by using a regularization method combined with the Galerkin method.

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