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Solutions for nth-order boundary value problems of impulsive singular nonlinear integro-differential equations in Banach spaces

Yanlai Chen1*, Tingqiu Cao1 and Baoxia Qin2

Author Affiliations

1 School of Economics, Shandong University, Jinan, Shandong, 250100, People’s Republic of China

2 Department of Mathematics, Qilu Normal University, Jinan, Shandong, 250013, People’s Republic of China

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Boundary Value Problems 2014, 2014:128  doi:10.1186/1687-2770-2014-128

Published: 20 May 2014

Abstract

Not considering the Green’s function, the present study starts to construct a cone formed by a nonlinear term in Banach spaces, and through the cone creates a convex closed set. We obtain the existence of solutions for the boundary values problems of nth-order impulsive singular nonlinear integro-differential equations in Banach spaces by applying the Mönch fixed point theorem. An example is given to illustrate the main results.

MSC: 45J05, 34G20, 47H10.

Keywords:
impulsive singular integro-differential equation; Banach spaces; boundary value problem; Mönch fixed point theorem; measure of noncompactness