Boundedness and asymptotic stability in the large of solutions of an ordinary differential system y′=f(t, y, y′). (1992)

• Record Type: Journal Article
• Authors: Venkatesulu, M.; Srinivasu, P. D. N.
• Is Part Of: Journal of applied mathematics and stochastic analysis. Volume 5:Number 3(1992)
• Page Start: 261
• Page End: 274
• Publication Date: 1992
• Subjects: existence -- unique -- solution -- continuous -- differentiable -- contraction -- system -- bounded -- stable -- uniform -- asymptotic -- exponential -- equi -- ultimate -- Lyapunov -- function; Mathematical models -- Periodicals; Computer simulation -- Periodicals; Computer science -- Mathematics -- Periodicals; Computer science -- Mathematics; Computer simulation; Mathematical models; Applied Mathematics; Periodicals; Electronic journals; 519.22
• DOI: 10.1155/S1048953392000212
• Languages: English
• ISSNs: 1048-9533

Abstract

Abstract : Differential equations of the form y ′ = f ( t, y, y ′ ), where f is not necessarily linear in its arguments, represent certain physical phenomena and solutions have been known for quite some time. The well known Clairut's and Chrystal's equations fall into this category. Earlier existence of solutions of first order initial value problems and stability of solutions of first order ordinary differential system of the above type were established. In this paper we study boundedness and asymptotic stability in the large of solutions of an ordinary differential system of the above type under certain natural hypotheses on f .