IJPAM: Volume 104, No. 3 (2015)

EXISTENCE AND OSGOOD TYPE UNIQUENESS OF MILD
SOLUTIONS OF NONLINEAR INTEGRODIFFERENTIAL
EQUATION WITH NONLOCAL CONDITION

Haribhau L. Tidke$^1$, Rupesh T. More$^2$
$^1$Department of Mathematics
School of Mathematical Sciences
North Maharashtra University
Jalgaon, 425 001, INDIA
$^2$Department of Mathematics
Arts, Commerce and Science College, Bodwad
Jalgaon, 425 310, INDIA


Abstract. The aim of the present paper is to study existence, Osgood type uniqueness and qualitative properties of mild solutions of nonlinear integrodifferential equation with nonlocal condition. The main tools employed in the analysis are based on the applications of the Leray-Schauder alternative, rely on a priori bounds of solutions and the well known Bihari's integral inequality.

Received: August 1, 2015

AMS Subject Classification: 34A12, 37C25, 34B10

Key Words and Phrases: existence and uniqueness, mild solutions, continuous dependence, boundedness, fixed point theorem, Bihari's integral inequality

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DOI: 10.12732/ijpam.v104i3.12 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2015
Volume: 104
Issue: 3
Pages: 437 - 460


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