Journal of Applied Mathematics and Stochastic Analysis
Volume 3 (1990), Issue 3, Pages 163-168

Existence and uniqueness of solutions of nonlocal problems for hyperbolic equation uxt=F(x,t,u,ux)

L. Byszewski

Department of Applied Mathematics, Florida Institute of Technology, Melbourne 32901, Florida, USA

Received 1 January 1990; Revised 1 May 1990

Copyright © 1990 L. Byszewski. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The aim of the paper is to give two theorems about existence and uniqueness of continuous solutions for hyperbolic nonlinear differential problems with nonlocal conditions in bounded and unbounded domains. The results obtained in this paper can be applied in the theory of elasticity with better effect than analogous known results with classical initial conditions.