Extremal solutions for the first order impulsive functional differential equations with upper and lower solutions in reversed order

This paper studies the existence of solutions of first order impulsive functional differential equations with lower and upper solutions in the reversed order, obtains the sufficient conditions for the existence of solutions by establishing a new comparison principle and using the monotone iterative technique. A concrete example is presented and solved to illustrate the obtained results.

[1]  Jifeng Chu,et al.  The monotone method for Neumann functional differential equations with upper and lower solutions in the reverse order , 2007 .

[2]  Jianhua Shen,et al.  Nonlinear boundary value problems for first order impulsive functional differential equations , 2007, Appl. Math. Comput..

[3]  J. Nieto,et al.  First-order impulsive ordinary differential equations with anti-periodic and nonlinear boundary conditions , 2000 .

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

[5]  J. Henderson,et al.  Upper and Lower Solution Methods for Fully Nonlinear Boundary Value Problems , 2002 .

[6]  V. Lakshmikantham,et al.  Nonlinear Integral Equations in Abstract Spaces , 1996 .

[7]  Wei Ding,et al.  Periodic boundary value problems for the first order impulsive functional differential equations , 2005, Appl. Math. Comput..

[8]  Zhiguo Luo,et al.  Periodic boundary value problem for first-order impulsive functional differential equations , 2008, Comput. Math. Appl..

[9]  Guotao Wang,et al.  Boundary value problems for systems of nonlinear integro-differential equations with deviating arguments , 2010, J. Comput. Appl. Math..

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

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

[12]  Juan J. Nieto,et al.  Boundary value problems for a class of impulsive functional equations , 2008, Comput. Math. Appl..

[13]  B. Ahmad,et al.  Existence and approximation of solutions for a class of nonlinear impulsive functional differential equations with anti-periodic boundary conditions , 2008 .

[14]  A. Cabada,et al.  Existence and Comparison Results for Difference φ-Laplacian Boundary Value Problems with Lower and Upper Solutions in Reverse Order , 2002 .

[15]  A. Cabada,et al.  Extremal solutions for third-order nonlinear problems with upper and lower solutions in reversed order , 2005 .

[16]  Jianhua Shen,et al.  Boundary value problems involving upper and lower solutions in reverse order , 2009 .

[17]  Wei Ding,et al.  Periodic boundary value problem for the second order impulsive functional differential equations , 2004, Appl. Math. Comput..

[18]  Mei Jia,et al.  Existence and uniqueness of solutions of second-order three-point boundary value problems with upper and lower solutions in the reversed order , 2008 .

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

[20]  Jianhua Shen,et al.  Periodic boundary value problems for delay differential equations with impulses , 2006 .

[21]  Tadeusz Jankowski Existence of solutions for second order impulsive differential equations with deviating arguments , 2007 .

[22]  P. Habets,et al.  Optimal Existence Conditions for φ-Laplacian Equations with Upper and Lower Solutions in the Reversed Order , 2000 .

[23]  D. Bainov,et al.  Impulsive Differential Equations: Periodic Solutions and Applications , 1993 .