Solutions for nth-order boundary value problems of impulsive singular nonlinear integro-differential equations in Banach spaces
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
Boundary Value Problems 2014, 2014:128 doi:10.1186/1687-2770-2014-128Published: 20 May 2014
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.