A note on the solvability of the nonlinear wave equation

Abstract

New existence and localization results for the nonlinear wave equation are established by means of the Schauder fixed point theorem. The main idea is to handle two equivalent operator forms of the wave equation, one of fixed point type giving the operator to which the Schauder theorem applies and an other one of coincidence type for the localization of a solution.

Keywords

• nonlinear wave equation
• nonlinear operator
• localization