Global existence and nonexistence of strong solutions to
pseudo-parabolic equations with variable exponents
Abstract
This paper deals with a pseudo-parabolic equation involving variable
exponents under Dirichlet boundary value condition. The authors first
develop the potential well method to prove a threshold result on the
existence and nonexistence of global solutions to the equations when
initial energy is less than the mountain pass level $d$. By borrowing
the idea from \cite{GW05,XS13} we also show some
existence and nonexistence results with high energy initial data. In
this case a new characterization for nonexistence of solution is given.
These results extend and improve a recent result obtained by Di et al.
(2017) \cite{DSP17} and Liao (2019)
\cite{Liao19,LGL19}.