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International Journal of Mathematics and Mathematical Sciences
Volume 12, Issue 3, Pages 539-545

On the exponential growth of solutions to non-linear hyperbolic equations

1Department of Mathematics, Pan American University, Edinburg 78509, Texas, USA
2Department of Mathematics, University of Kentucky, Lexington 40506, Kentucky, USA

Received 9 September 1987

Copyright © 1989 Hindawi Publishing Corporation. 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.


Existence-uniqueness theorems are proved for continuous solutions of some classes of non-linear hyperbolic equations in bounded and unbounded regions. In case of unbounded region, certain conditions ensure that the solution cannot grow to infinity faster than exponentially.