Nonlinear boundary value problem of first order impulsive functional differential equations

Abstract

This paper discusses nonlinear boundary value problem for first order impulsive functional differential equations. We establish several existence results by using the lower and upper solutions and monotone iterative techniques. Two examples are discussed to illustrate the efficiency of the obtained results.  2005 Elsevier Inc. All rights reserved.

Multi-point boundary value problem for first order impulsive integro-differential equations with multi-point jump conditions

“…The monotone iterative technique coupled with the method of lower and upper solutions is a powerful method used to approximate solutions of several nonlinear problems (see [4][5][6][7][8][9][10][11][12][13][14]). Boundary value problems for first order impulsive functional differential equations with lower and upper solutions in reversed order have been widely discussed in recent years (see [15][16][17][18][19][20]). However, the discussion of multi-point boundary value problems for first order impulsive functional differential equations is very limited (see [21]).…”

Existence of three solutions for impulsive multi-point boundary value problems

“…There has been increasing interest in the investigation for boundary value problems of nonlinear impulsive differential equations during the past few years, and many works have been published about the existence of solutions for second-order impulsive differential equations. There are some common techniques to approach these problems: Fixed point theorems [8,9,31], the method of upper and lower solutions [7], and topological degree theory [37]. In the last few years, variational methods and critical point theory have been used to determine the existence of solutions for impulsive differential equations under certain boundary conditions, see [1,21,43,44,46,48] and the references therein.…”

Multiple positive solutions to multipoint one-dimensional p-Laplacian boundary value problem with impulsive effects

“…The boundary value problems for impulsive differential equations have been studied extensively in literature (see [2]- [9], [11], [12], [14] and the references therein). Most of those papers have studied the two-point or periodic boundary value problems for impulsive differential equations.…”