International Journal of Mathematics and Mathematical Sciences
Volume 22 (1999), Issue 3, Pages 569-571
doi:10.1155/S0161171299225690
Bounded and L2-solutions to a second order nonlinear differential equation with a square integrable forcing term
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Received 12 May 1998
Copyright © 1999 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
This paper presents two theorems concerning the nonlinear differential equation x″+c(t)f(x)x′+a(t,x)=e(t), where e(t) is a continuous square-integrable function. The first theorem gives sufficient conditions when all the solutions of this equation are bounded while the second theorem discusses when all the solutions are in L2[0,∞).