Positive Solutions of Initial Value Problem for the Systems of Second Order Integro-Differential Equations in Banach Space

Authors: Lv Yuhua

Abstract:

In this paper, by establishing a new comparison result, we investigate the existence of positive solutions for initial value problems of nonlinear systems of second order integro-differential equations in Banach space.We improve and generalize some results  (see[5,6]), and the results is new even in finite dimensional spaces.

Keywords: Systems of integro-differential equations, monotone iterative method, comparison result, cone.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1335776

References:

[1] Guo Dajun. Initial value problem for second-order integro-differential equation in Banach space(J).Nonlinear Analysis,1999,37:289-300.
[2] Chen F.Q, Chen Y.S, On monotone iterative method for initial value problems of nonlinear second order integro-differential equations in Banach spaces , Applied Mathematics and Mechanics,2000,21(5):459- 467(in Chinese).
[3] Liu Lishan.Iterative method for solutiona and coupled quasi-solutions of nonlinear integro-differential equations of mixed type in Banach spaces .Nonlinear Analysis,2000,42:583-598.
[4] Guo Lin.Boundary value problems for second-order integrodifferential equations in Bannach space(J). Acta Analysis Functionalis Applicata,2002,4(3):204-210.
[5] Song Guangxing.The solutions of initial value problems for second order integro-differential equations in Banach space(J). Acta Mathematatica Sinica, 2004, 47(1) 71-78.
[6] Song Guangxing.Initial value problems for the systems of second order integro-differential equations in Banach space(J). Acta Mathematatica Scientia, 2008, 28A(6) 1119-1127.
[7] Dajun Guo,V.Lakshmikantham, Xinzhi Liu. Nolinear Integral Equations in Abstract Spaces. Dordrecht:Kluwer Academic Publishers,1996.