International Journal of Mathematics and Mathematical Sciences
Volume 12 (1989), Issue 3, Pages 539-545
doi:10.1155/S0161171289000670
On the exponential growth of solutions to nonlinear hyperbolic equations
H. Chi1
, H. Poorkarimi1
, J. Wiener1
and S.M. Shah4
1Department of Mathematics, Pan American University, Edinburg 78509, Texas, USA
4Department of Mathematics, University of Kentucky, Lexington 40506, Kentucky, USA
Abstract
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.