Open AccessExistence and uniqueness of mild and strong solutions of nonlinear volterra integrodifferential equations in Banach spaces
Author(s) -
H. L. Tidke,
M. B. Dhakne
Publication year - 2010
Publication title -
demonstratio mathematica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.541
H-Index - 28
eISSN - 2391-4661
pISSN - 0420-1213
DOI - 10.1515/dema-2013-0253
Subject(s) - mathematics , uniqueness , banach space , nonlinear system , fixed point theorem , semigroup , picard–lindelöf theorem , banach fixed point theorem , mathematical analysis , volterra integral equation , pure mathematics , integral equation , quantum mechanics , physics
In this paper we prove the existence and uniqueness of mild and strong solutions of a nonlinear Volterra integrodifferential equation with nonlocal condition. Our analysis is based on semigroup theory and Banach fixed point theorem and inequalities are established by Gronwall and B. G. Pachpatte.