Global existence and stability of solution for a p-Kirchhoff type hyperbolic equation with damping and source terms

"In this paper, we consider a nonlinear $p-$Kirchhoff type hyperbolic equation with damping and source terms $$u_{tt}-M\left( \underset{\Omega }{\int }\left\vert \nabla u\right\vert ^{p}dx\right) \Delta _{p}u+\left\vert u_{t}\right\vert ^{m-2}u_{t}=\left\vert ^{r-2}u.$$ Under suitable assumptions positive initial energy, prove the global existence of solution by using potential energy Nehari's functionals. Finally, stability is established based on Komornik's integral inequality."