International Journal of Mathematics and Mathematical Sciences
Volume 18 (1995), Issue 4, Pages 823-824

General boundedness theorems to some second order nonlinear differential equation with integrable forcing term

Allan Kroopnick

Office of Retirement & Survivors Insurance, Social Security Administration, 3-D-21 Operations Building, 6401 Security Boulevard, Baltimore 21235, MD, USA

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.


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.