On the solvability of periodic boundary value problems with impulse

On the Solvability of Periodic Boundary Value Problems with Impulse

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.

On the solvability of anti-periodic boundary value problems with impulse

Impulsive differential equations, which arise in biology, physics, population dynamics, economics, etc., are a basic tool to study evolution processes that are subjected to abrupt in their states (see [8-12]). Recently, the existence results were extended to anti-periodic boundary value problems for first-order impulsive differential equations [13,14]. Very recently, Wang and Shen [15] investig...

Nonmonotone Impulse Effects in Second-order Periodic Boundary Value Problems

We deal with the nonlinear impulsive periodic boundary value problem u′′ = f (t,u,u′), u(ti+) = Ji(u(ti)), u′(ti+) = Mi(u′(ti)), i= 1,2, . . . ,m, u(0) = u(T), u′(0) = u′(T). We establish the existence results which rely on the presence of a well-ordered pair (σ1,σ2) of lower/upper functions (σ1 ≤ σ2 on [0,T]) associated with the problem. In contrast to previous papers investigating such proble...

Solvability of Nonlocal Fractional Boundary Value Problems

On the Solvability of Nonlinear, First-Order Boundary Value Problems

This article investigates the existence of solutions to first-order, nonlinear boundary value problems (BVPs) involving systems of ordinary differential equations and two-point boundary conditions. Some sufficient conditions are presented that will ensure solvability. The main tools employed are novel differential inequalities and fixed-point methods. AMS 2000 Classification: 34B15, 34B99