Existence of solution for a class of nonvariational Kirchhoff type problem via dynamical methods

Stability of solutions for a parabolic problem involving fractional p-Laplacian with logarithmic nonlinearity

“…In recent years, the global existence and blow-up of solutions to the following model (M 1 )    u t − ∆u = f (u), x ∈ Ω, t > 0, u(x, t) = 0, x ∈ ∂Ω, t > 0, u(x, 0) = u 0 (x), x ∈ Ω has been studied extensively by many authors, see for example ( [41], [26], [36], [20], [2]) and the references therein where the authors have assumed the following conditions on the nonlinearity f (u) :…”

“…To do this end, let θ be the nonnegative function which belongs to C([0, T * ]). From (3.12) we have In this section, by using the potential well theory combined with the Nehari manifold, we prove that the local weak solutions of problem (1.1) exist globally, see ( [2], [42]) and the references therein for some results on global existence of solutions. Furthermore, we show that the norm u(t) 2 decays polynomially.…”

Global well‐posedness and finite time blow‐up for a class of wave equation involving fractionalp‐Laplacian with logarithmic nonlinearity

“…In this section, by means of a differential inequality technique, we prove that the local solutions of problem (1.1) blow‐up in finite time. see [2, 43, 45] and the references therein for some results on blow‐up of solutions.…”

Global existence and blow-up of solutions for a parabolic equation involving the fractional $p(x)$-Laplacian

“…In this section by combining the potential well theory with the Nehari manifold, we prove that the local solutions of problem (1.1) can be extended to global solutions, see ( [2], [3] [35], [19]) and the references therein for some results on the existence of global solutions.…”