Kroopnick (2010) discussed the bounded solutions of certain non-autonomous differential equations of the second order by using the integral test. In this paper, instead of the integral test, we study the results of Kroopnick  by using the Liapunov’s function approach. We compare the established results with that of Kroopnick . We also give some additional results on the equi-bounded solutions and uniformly-bounded solutions, and an example is given for the illustrations.
Digital Object Identifier (DOI)
"A Note on the Bounded Solutions to x′′+c(t, x, x′)+q(t)b(x) = f (t),"
Applied Mathematics & Information Sciences: Vol. 08:
1, Article 49.
Available at: https://digitalcommons.aaru.edu.jo/amis/vol08/iss1/49