A note on the solvability of the nonlinear wave equation
Keywords:nonlinear wave equation, nonlinear operator, localization
AbstractNew 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.
Granas, A. and Dugundji, J., Fixed Point Theory, Springer, New York, 2003.
Lions, J. L. and Magenes, E., Problèmes aux limites non homogènes 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.
How to Cite
Copyright (c) 2015 Journal of Numerical Analysis and Approximation Theory
This work is licensed under a Creative Commons Attribution 4.0 International License.
Open Access. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.