On an Initial Boundary Value Problem for a Class of Odd Higher Order Pseudohyperbolic Integrodifferential Equations

This paper is devoted to the study of the well-posedness of an initialboundary value problem for an odd higher order nonlinear pseudohyperbolic integrodifferential partial differential equation. We associate to theequation n nonlocal conditions and n+1 classical conditions. Upon some a priori estimates and density arguments, we first establish the existenceand uniqueness of the strongly generalized solution in a class of a certaintype of Sobolev spaces for the associated linear mixed problem. On thebasis of the obtained results for the linear problem, we apply an iterativeprocess in order to establish the well-posedness of the nonlinear problem