Integral boundary value problems with causal operators

This paper considers the existence of solutions for a class of integral boundary value problems with causal operators. We build a new comparison theorem. By utilizing the monotone iterative technique and the method of lower and upper solutions, we formulate sufficient conditions under which such problems have extremal or quasisolutions in a corresponding sector.

[1]  Guangxing Song,et al.  Extremal solutions of periodic boundary value problems for first order integro-differential equations of mixed type , 2004 .

[2]  Weibing Wang,et al.  Multi-point boundary value problems for second-order functional differential equations , 2008, Comput. Math. Appl..

[3]  Guotao Wang,et al.  Integral boundary value problems for first order integro-differential equations with deviating arguments , 2009 .

[4]  Tadeusz Jankowski,et al.  Boundary value problems with causal operators , 2008 .

[5]  V. Lakshmikantham,et al.  Monotone iterative techniques for nonlinear differential equations , 1985 .

[6]  T. Jankowski.  Differential equations with integral boundary conditions , 2002 .

[7]  V. Lakshmikantham,et al.  Theory of Impulsive Differential Equations , 1989, Series in Modern Applied Mathematics.

[8]  Donal O'Regan,et al.  Existence of solutions for first order ordinary differential equations with nonlinear boundary conditions , 2004, Appl. Math. Comput..

[9]  J. Vasundhara Devi,et al.  Monotone iterative technique for periodic boundary value problems with causal operators , 2006 .

[10]  Xiaoming He,et al.  Periodic boundary value problems for first order impulsive integro-differential equations of mixed type , 2004 .

[11]  Juan J. Nieto,et al.  New comparison results for impulsive integro-differential equations and applications , 2007 .

[12]  Jianhua Shen,et al.  Periodic boundary value problem for the first order impulsive functional differential equations , 2007 .

[13]  Fengjie Geng,et al.  Differential equations involving causal operators with nonlinear periodic boundary conditions , 2008, Math. Comput. Model..

[14]  Constantin Corduneanu,et al.  Functional Equations with Causal Operators , 2002 .

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

[16]  Wei Ding,et al.  Anti-periodic boundary value problems for first order impulsive functional differential equations , 2007, Appl. Math. Comput..