# Existence and localization results for the nonlinear wave equation

## Abstract

Existence and localization results for the nonlinear wave equation are established by Krasnoselskii’s compression-expansion fixed point theorem in cones. The main idea is to handle two equivalent operator forms of the wave equation, one of fixed point type giving the operator to which Krasnoselskii’s theorem applies and an other one of coincidence type for the localization of a solution. In this way, the compression-expansion technique is extended from scalar equations to abstract equations, specifically to partial differential equations.

## Authors

Department of Mathematics, Babes-Bolyai University, Cluj-Napoca, Romania

## Keywords

Wave equation, fixed point, cone.

## Paper coordinates

R. Precup, Existence and localization results for the nonlinear wave equation, Fixed Point Theory 5 (2004), 309-321.

## PDF

##### Journal

Fixed Point Theory and Applications

##### Online ISSN

MR2117341, Zbl 1107.35086.