A unique positive solution for nth-order nonlinear impulsive singular integro-differential equations on unbounded domains in Banach spaces

In this paper, the fixed point theory combined with a monotone iterative technique is used to investigate the unique positive solution of a boundary problem for nth-order nonlinear impulsive singular integro-differential equations of mixed type on an infinite interval in a Banach space. The conditions for the existence of a unique positive solution are established. In addition, an explicit iterative sequence for approximating the solution of the boundary value problem is derived together with an error estimate. Furthermore, the conditions of the theorems can be easily verified.

[1]  Bao Gang Xu,et al.  A structural theorem on embedded graphs and its application to colorings , 2009 .

[2]  Kok Lay Teo,et al.  An optimal control problem involving impulsive integrodifferential systems , 2007, Optim. Methods Softw..

[3]  Dajun Guo.  Boundary value problems for impulsive integro-differential equations on unbounded domains in a Banach space , 1999, Appl. Math. Comput..

[4]  Congxin Wu,et al.  A unique solution of initial value problems for first order impulsive integro-differential equations of mixed type in Banach spaces , 2002 .

[5]  Dajun Guo.  Existence of solutions for nth-order integro-differential equations in Banach spaces , 2001 .

[6]  Solving an identification problem as an impulsive optimal parameter selection problem , 2005 .

[7]  Dajun Guo.  Initial Value Problems for Nonlinear Second Order Impulsive Integro-differential Equations in Banach Spaces , 1996 .

[8]  Lishan Liu,et al.  Initial value problems for nonlinear second order impulsive integro-differential equations of mixed type in Banach spaces , 2006 .

[9]  Lishan Liu,et al.  On well-posedness of an initial value problem for nonlinear second-order impulsive integro-differential equations of Volterra type in Banach spaces , 2006 .

[10]  Dajun Guo,et al.  Existence of positive solutions for nth-order nonlinear impulsive singular integro-differential equations in Banach spaces☆ , 2008 .

[11]  Lishan Liu,et al.  Iterative method for solutions and coupled quasi-solutions of nonlinear integro-differential equations of mixed type in Banach spaces , 2000 .

[12]  D. Guo.  Solutions of nonlinear integrodifferential equations of mixed type in Banach spaces , 1989 .

[13]  Dajun Guo,et al.  Multiple positive solutions for nth-order impulsive integro-differential equations in Banach spaces , 2005 .

[14]  Dajun Guo.  Existence of solutions for nth order impulsive integro-differential equations in a Banach space , 2001 .

[15]  W. Ames,et al.  Nonlinear problems in abstract cones , 1988 .

[16]  Dajun Guo,et al.  Extremal solutions for nth-order impulsive integro-differential equations on the half-line in Banach spaces , 2006 .