Global existence and finite time blowup for a mixed pseudo-parabolic p-Laplacian type equation

Initial boundary value problem of pseudo‐parabolic Kirchhoff equations with logarithmic nonlinearity

“…It is worth pointing out that the nonlinear terms in () make the local existence of solutions nontrivial. What makes us most delightful is that some excellent works provide ideas to deal with the local existence of solutions for (), like the Galerkin method in [58], the Schauder fixed point theory in [59], the contraction mapping principle in [60]. Here, by using the argument similar to [58], we prove that () admits local weak solutions in Definition 2.1.…”

“…In fact when $$$ 1<p\le 2 $$$, $$$ {2}^{\ast }+2p\left(1-\frac{2^{\ast }}{p^{\ast }}\right)\le {p}^{\ast } $$$, when $$$ p>2 $$$, $$$ {2}^{\ast }+2p\left(1-\frac{2^{\ast }}{p^{\ast }}\right)<{p}^{\ast } $$$. The interval we set for $$$ q $$$ is a bit larger than $$$ q+1\le {2}^{\ast } $$$ in [60].…”