Existence and stability solutions of nonlinear stochastic functional partial integrodifferential equations with infinite delay. (2016)

• Record Type: Journal Article
• Authors: Parthasarathy, Chinnasamy; Arjunan, M. Mallika; Vinodkumar, A.
• Is Part Of: International journal of mathematics in operational research. Volume 9:Number 1(2016)
• Page Start: 65
• Page End: 78
• Publication Date: 2016
• Subjects: existence -- uniqueness -- stability -- successive approximation -- Bihari&amp -- #39 -- s inequality -- resolvent operators -- nonlinear integrodifferential equations -- stochastic integrodifferential equations -- functional integrodifferential equations -- infinite delay -- non-Lipschitz condition -- partial integrodifferential equations; Operations research -- Mathematical models -- Periodicals; Operations research -- Mathematics -- Periodicals; Decision making -- Mathematical models -- Periodicals; 658.4033
• Languages: English
• ISSNs: 1757-5850

Abstract

In this paper, we are focused upon the results on existence, uniqueness and stability of mild solution for stochastic functional integrodifferential equations with non-Lipschitz condition. The theory of resolvent operator is utilised to exhibit the existence of these mild solutions. The results are obtained by using the method of successive approximation and Bihari's inequality. Finally, an example is provided for demonstration.