On the solvability of periodic boundary value problems with impulse

Abstract

In this work we obtain some new results concerning the existence of solutions to an impulsive first-order, nonlinear ordinary differential equation with periodic boundary conditions. The ideas involve differential inequalities and Schaefer's fixed-point theorem.

Variational analysis to fourth-order impulsive differential equations

“…For an introduction of the basic theory of impulsive differential equations in R n , see [3], [8], and [13]. Some classical tools have been used to study such problems in the literature, such as the coincidence degree theory of Mawhin, the method of upper and lower solutions with the monotone iterative technique, and some fixed point theorems in cones (see [7,9,12]). …”

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.…”

Antiperiodic Boundary Value Problems for Second-Order Impulsive Ordinary Differential Equations

“…Many literatures have been published about existence of solutions for first-order and second-order impulsive ordinary differential equations with boundary conditions [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] , which are important for complementing the theory of impulsive equations. In recent years, the solvability of the antiperiodic boundary value problems of first-order and second-order differential equations were studied by many authors, for example, we refer to 20-32 and the references therein.…”