Title: Existence and stability solutions of nonlinear stochastic functional partial integrodifferential equations with infinite delay

Authors: Chinnasamy Parthasarathy; M. Mallika Arjunan; A. Vinodkumar

Addresses: Department of Mathematics, Sri Shakthi Institute of Engineering and Technology, Coimbatore-641 062, Tamil Nadu, India ' Department of Mathematics, CBM College, Kovaipudur, Coimbatore-641 042, Tamil Nadu, India ' Department of Mathematics, PSG College of Technology, Coimbatore-641 004, Tamil Nadu, India

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.

Keywords: existence; uniqueness; stability; successive approximation; Bihari's inequality; resolvent operators; nonlinear integrodifferential equations; stochastic integrodifferential equations; functional integrodifferential equations; infinite delay; non-Lipschitz condition; partial integrodifferential equations.

DOI: 10.1504/IJMOR.2016.077561

International Journal of Mathematics in Operational Research, 2016 Vol.9 No.1, pp.65 - 78

Received: 24 Jul 2014
Accepted: 22 Aug 2014
Published online: 06 Jul 2016 *

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