Global existence and stability of solution for a p−Kirchhoff type hyperbolic equation with damping and source terms - OUAOUA, Amar; KHALDI, Aya; MAOUNI, Messaoud (Studia Universitatis Babeș-Bolyai Mathematica, 2022)
In this paper, we consider a nonlinear p−Kirchhoff type hyperbolic equation with damping and source terms f utt − M  Ω |∇u|p  dx ∆pu + |ut| m−2 ut = |u| r−2 u. Under suitable assumptions and positive initial energy, we prove the global existence of solution by using the potential energy and Nehari’s functionals. Finally, the stability of equation is established based on Komornik’s integral inequality. Mathematics Subject Classification (2010): 35L70, 35L05, 35B40, 93D20. Received 30 December 2019; Accepted 03 February 2020.