A Note on the Bounded Solutions to x '' plus c(t, x, x ') plus q(t)b(x) = f(t)

Tunc C.

APPLIED MATHEMATICS & INFORMATION SCIENCES, vol.8, no.1, pp.393-399, 2014 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 8 Issue: 1
  • Publication Date: 2014
  • Journal Name: APPLIED MATHEMATICS & INFORMATION SCIENCES
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.393-399
  • Van Yüzüncü Yıl University Affiliated: Yes

Abstract

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 [9] by using the Liapunov's function approach. We compare the established results with that of Kroopnick [9]. We also give some additional results on the equi-bounded solutions and uniformly-bounded solutions, and an example is given for the illustrations.