### Electronic Research Archive

2020, Issue 2: 651-669. doi: 10.3934/era.2020034
Special Issues

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

• 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.

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

### Related Papers:

• 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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