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

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.