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.
Department of Mathematics, Babes-Bolyai University, Cluj-Napoca, Romania
Nonlinear wave equation; nonlinear operator; localization
R. Precup, A note on the solvability of the nonlinear wave equation, Rev. Anal. Numér. Théor. Approx. 33 (2004) no. 2, 237-241.
Revue d’analyse numérique et de théorie d’approximation
ISSN 1222-9024, ISSN-L 1222-9024, ISSN-E 2457-8126
MR2192473, Zbl pre05003794.
google scholar link
 Granas, A. and Dugundji, J., Fixed Point Theory, Springer, New York, 2003.
 Lions, J. L. and Magenes, E., Problemes aux limites non homogenes et applications, vol. 1, Dunod, Paris, 1968.
 Precup, R., Methods in Nonlinear Integral Equations, Kluwer, Dordrecht, 2002.
 Precup, R., Lectures on Partial Differential Equations (in Romanian), Cluj University Press, in print.
 Precup, R., Existence and localization results for the nonlinear wave equation, to appear.