Open AccessOn stochastic integrodifferential equations via non-linear integral contractors II
Author(s) -
Miljana Jovanović,
Svetlana Janković
Publication year - 2010
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil1002081j
Subject(s) - mathematics , lipschitz continuity , uniqueness , equivalence (formal languages) , continuation , integral equation , volterra integral equation , mathematical analysis , pure mathematics , computer science , programming language
The present paper represents a continuation of paper [4], in which the existence and uniqueness problems for a general Ito-Volterra integrodifferential equation are investigated by using the concept of a non-linear random integral contractor. Since the Lipschitz condition and the random integral contractor for the coefficients of the considered equation, in general, cannot be compared, the notions of the modified Lipschitz condition and modified integral contractor are introduced on some function spaces, as well as the conditions of their equivalence. Some existence and uniqueness theorems are also given. 2010 Mathematics Subject Classifications. 60H20. .