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

Abstract

<abstract> <p>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.</p> </abstract>