Global existence and finite time blow-up for a class of fractional $ p $-Laplacian Kirchhoff type equations with logarithmic nonlinearity

Fugeng Zeng; Peng Shi; Min Jiang; Fugeng Zeng; Peng Shi; Min Jiang

doi:10.3934/math.2021155

AIMS Mathematics

2021, Volume 6, Issue 3: 2559-2578. doi: 10.3934/math.2021155

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Research article

Global existence and finite time blow-up for a class of fractional $ p $-Laplacian Kirchhoff type equations with logarithmic nonlinearity

School of Date Sciences and Information Engineering, Guizhou Minzu University, Guizhou, China

Received: 15 October 2020 Accepted: 21 December 2020 Published: 23 December 2020
MSC : 39A13, 34B18, 34A08

In this paper, we study the initial-boundary value problem for a class of fractional $ p $-Laplacian Kirchhoff diffusion equation with logarithmic nonlinearity. For both subcritical and critical states, by means of the Galerkin approximations, the potential well theory and the Nehari manifold, we prove the global existence and finite time blow-up of the weak solutions. Further, we give the growth rate of the weak solutions and study ground-state solution of the corresponding steady-state problem.
- Kirchhoff type,
- $ p $-Laplacian,
- fractional,
- global existence,
- blow-up,
- ground-state solution
Citation: Fugeng Zeng, Peng Shi, Min Jiang. Global existence and finite time blow-up for a class of fractional $ p $-Laplacian Kirchhoff type equations with logarithmic nonlinearity[J]. AIMS Mathematics, 2021, 6(3): 2559-2578. doi: 10.3934/math.2021155

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Abstract

In this paper, we study the initial-boundary value problem for a class of fractional $ p $-Laplacian Kirchhoff diffusion equation with logarithmic nonlinearity. For both subcritical and critical states, by means of the Galerkin approximations, the potential well theory and the Nehari manifold, we prove the global existence and finite time blow-up of the weak solutions. Further, we give the growth rate of the weak solutions and study ground-state solution of the corresponding steady-state problem.

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