Solvability of nonlinear hyperbolic equation with nonlinear integral Neumann conditions

Abstract

In this paper, we examine a nonlinear hyperbolic equation with a nonlinear integral condition, where we prove the existence and the uniqueness of the linear problem by the Faedo-Galerkin method. By applying an iterative process to some significant results obtained for the linear problem, the existence and the uniqueness of the weak solution for the nonlinear problem are additionally examined.