Existence of solutions for first order PBVPs with impulses on time scales

In this paper, we consider some kind of nonlinear periodic differential equation with impulses on time scales, and give some new criteria for the existence of at least one solution by using differential inequalities and fixed point theorems.

[1]  Ravi P. Agarwal,et al.  Multiple positive solutions of singular Dirichlet problems on time scales via variational methods , 2007 .

[2]  R. Agarwal,et al.  Basic properties of Sobolev's spaces on time scales , 2006 .

[3]  R. Agarwal,et al.  Basic Calculus on Time Scales and some of its Applications , 1999 .

[4]  Juan J. Nieto,et al.  A Contribution to the Study of Functional Differential Equations with Impulses , 2000 .

[5]  Christopher C. Tisdell,et al.  Existence of solutions to first-order periodic boundary value problems , 2006 .

[6]  J. Nieto.  Periodic boundary value problems for first-order impulsive ordinary differential equations , 2002 .

[7]  A. Peterson,et al.  Inequalities on Time Scales: A Survey , 2001 .

[8]  Ravi P. Agarwal,et al.  Existence of multiple positive solutions for second order nonlinear dynamic BVPs by variational methods , 2007 .

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

[10]  Juan J. Nieto,et al.  Impulsive resonance periodic problems of first order , 2002, Appl. Math. Lett..

[11]  D. R. Smart.  Fixed Point Theorems , 1974 .

[12]  H. Thompson,et al.  On the existence of solutions to boundary value problems on time scales , 2005 .

[13]  G. Guseinov,et al.  On Green's functions and positive solutions for boundary value problems on time scales , 2002 .

[14]  Juan J. Nieto,et al.  Basic Theory for Nonresonance Impulsive Periodic Problems of First Order , 1997 .

[15]  A. Peterson,et al.  Dynamic Equations on Time Scales , 2001 .

[16]  Rong Yuan,et al.  On the solvability of periodic boundary value problems with impulse , 2007 .

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

[18]  C. Tisdell,et al.  EXISTENCE AND UNIQUENESS OF SOLUTIONS TO FIRST-ORDER SYSTEMS OF NONLINEAR IMPULSIVE BOUNDARY-VALUE PROBLEMS WITH SUB-, SUPER-LINEAR OR LINEAR GROWTH , 2007 .

[19]  J. Nieto,et al.  Impulsive periodic boundary value problems of first-order differential equations , 2007 .