First- and second-order dynamic equations with impulse

Fm Atici,Dc Biles

doi:10.1155/ade.2005.119

Abstract

We present existence results for discontinuous first- and continuous second-order dynamic equations on a time scale subject to fixed-time impulses and nonlinear boundary conditions.

Highlights

We first briefly survey the recent results for existence of solutions to first-order problems with fixed-time impulses
Assuming the existence of a lower and an upper solution, we prove that the solution of the boundary value problem stays between them
We introduce the concept of lower and upper solutions of problem (3.1)–(3.5) as follows

Summary

Introduction

We first briefly survey the recent results for existence of solutions to first-order problems with fixed-time impulses. Assume that conditions (1)–(5) are satisfied and α, β are lower and upper solutions of (2.1)–(2.3) with α(t) ≤ β(t) for all t ∈ J.

Results

Conclusion