Stability of solutions of a nonstandard ordinary differential system by Lyapunov's second method. (1991)

• Record Type: Journal Article
• Authors: Venkatesulu, M.; Srinivasu, P. D. N.
• Is Part Of: Journal of applied mathematics and stochastic analysis. Volume 4:Number 3(1991)
• Page Start: 211
• Page End: 224
• Publication Date: 1991
• Subjects: nonstandard -- initial -- value -- problem -- existence -- unique -- solution -- continuous -- differentiable -- contraction -- system -- stable -- uniform -- asymptotic; 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/S1048953391000175
• 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 are known for quite some time. The well known Clairut's and Chrystal's equations fall into this category. Earlier we established the existence of a (unique) solution of the nonstandard initial value problem y ′ = f ( t, y, y ′ ), y ( t 0 ) = y 0 under certain natural hypotheses on f . In this paper, we studied the stability of solutions of a nonstandard first order ordinary differential system.