Classical solutions for a class of nonlinear wave equations

Abstract

We study a class of initial value problems subject to nonlinear partial differential equations of hyperbolic type. A new topological approach is applied to prove the existence of nontrivial nonnegative solutions. More precisely, we propose a new integral representation of the solutions for the considered initial value problems and using this integral representation we establish existence of classical solutions for the considered classes of nonlinear wave equations.

Keywords

• hyperbolic equations
• nonnegative solution
• fixed point
• cone
• sum of operators