Further results on periodic boundary value problems for nonlinear first order impulsive functional differential equations

Abstract

This paper is concerned with the solvability of periodic boundary value problems for nonlinear impulsive functional differential equationsWe obtain sufficient conditions for the existence of at least one solution of problem ( * ) at resonance and nonresonance cases, respectively. Examples are presented to illustrate the main results.

Existence of Solutions for Second-Order Nonlinear Impulsive Differential Equations with Periodic Boundary Value Conditions

“…Our approach using differential inequalities is based on ideas in [24,25]. Moreover, our new results complement and extend those of [26][27][28] in the sense that we allow superlinear growth of f (t, p, q) in p and q .…”

Existence of Solutions of Multi-Point BVPs for Impulsive Functional Differential Equations with Nonlinear Boundary Conditions

“…In recent years, there has been a large number of papers concerned with the solvability of periodic boundary value problems for first order [1][2][3][4][5][6][7][8][9][10][11][12]16,18,20,[22][23][24][25][26][27][29][30][31], second order or higher order [13][14][15][16] impulsive functional differential equations. To illustrate the motivation of this paper and compare the results in this paper to known ones, we first present a survey on studies on boundary value problems for first order ordinary or functional differential equations with or without impulses effects.…”

“…In a recent paper [23], Liu studied the following periodic boundary value problem of first order impulsive functional differential equation…”

“…Sufficient conditions for the existence of at least one solution of above mentioned IBVP were established in [23].…”

“…New results on the existence of solutions of IBVP(1.8) and IBVP(1.9) are established, respectively. The technical methods used are motivated by [23] and are different from those in [2,18,16,19,25,9,26,21,27].…”