International Journal of Mathematics and Mathematical Sciences
Volume 18 (1995), Issue 4, Pages 823-824
doi:10.1155/S0161171295001050
General boundedness theorems to some second order nonlinear differential equation with integrable forcing term
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Received 1 November 1991; Revised 12 January 1995
Copyright © 1995 Allan Kroopnick. 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.
Abstract
In this note we present a boundedness theorem to the equation
x″+c(t,x,x′)+a(t)b(x)=e(t) where e(t) is a continuous absolutely integrable function over the
nonnegative real line. We then extend the result to the equation x″+c(t,x,x′)+a(t,x)=e(t). The
first theorem provides the motivation for the second theorem. Also, an example illustrating the theory is
then given.