First-order Impulsive Differential Equations Research Articles

Periodic boundary value problem for first-order impulsive functional differential equations

This paper discusses the periodic boundary value problem for a class of first-order impulsive functional differential equations. We establish several existence results under weaker hypotheses by using the Leray–Schauder alternative, the lower and upper solution method and the monotone iterative technique. The corresponding results in the literature are improved or extended, some examples are also given to illustrate the advantage of the results.

On functional improper Volterra integral equations and impulsive differential equations in ordered Banach spaces

In this paper we derive existence and comparison results for discontinuous improper functional integral equations of Volterra type in an ordered Banach space which has a regular order cone. For this purpose we prove Dominated and Monotone Convergence Theorems for improper integrals. The obtained results are then applied to first-order impulsive differential equations. Concrete examples are also solved by using symbolic programming.

Oscillation criteria for first-order impulsive differential equations with positive and negative coefficients

Some sufficient conditions are obtained for oscillation of all solutions of the first-order impulsive differential equation with positive and negative coefficients [ x ( t ) - R ( t ) x ( t - r ) ] ′ + P ( t ) x ( t - τ ) - Q ( t ) x ( t - σ ) = 0 , τ ⩾ σ > 0 , t ⩾ t 0 , x ( t k + ) = I k ( x ( t k ) ) , k = 1 , 2 , … . Our results improve the known results in the literature.

Periodic Boundary Value Problem for First Order Impulsive Differential Equation at Resonance

We develop a general theorem concerning the existence of solutions to the periodic boundary value problem for the first-order impulsive differential equation,    x′(t) = f(t, x(t)), t ∈ J {t1, t2, · · · , tk} 4x(ti) = Ii(x(ti)), i = 1, 2 · · · k x(0) = x(T ). And using it we get a concrete existence result. Moreover, to our knowledge the coincidence degree method has not been used to the first order impulsive differential systems. Besides, our results can also be applied in studying the usual periodic boundary value problem at resonance without impulses.

First-order impulsive ordinary differential equations with advanced arguments

This paper deals with impulsive advanced ordinary differential equations with boundary conditions. We investigate the existence of solutions and quasisolutions for advanced impulsive differential equations. To obtain such results we apply Schauder's fixed point theorem. Corresponding results are also formulated for differential inequalities.

Multiplicity Positive Solutions to Periodic Problems for First-Order Impulsive Differential Equations

This paper is devoted to studying the existence of single and multiple positive solutions to periodic problems for first-order impulsive differential equations. In addition, we apply our existence theorems to nonlinear periodic problems with singularity at the origin. Our proofs are based on Krasnoselskii fixed-point theorem in cones.

Nonhomogeneous boundary value problem for first-order impulsive differential equations with delay

The authors employ the method of upper and lower solution coupled with the monotone iterative technique to obtain results of existence and uniqueness for a nonhomogeneous boundary value problem of impulsive differential equations with delay.

Periodic boundary value problem for non-Lipschitzian impulsive functional differential equations

We consider a class of first-order impulsive functional differential equations, where the functional dependence is not necessarily a Lipschitzian function. The new maximum principle improves and extends previous results and uniqueness of solution between a lower and an upper solution for a particular nonlinear problem is presented. We give conditions for existence of extremal solutions in an interval delimited by a lower and an upper solution.

Antiperiodic boundary value problem for first-order impulsive ordinary differential equations

This paper discusses the antiperiodic boundary value problem for first-order impulsive ordinary differential equations. We establish several existence results by using the Leray-Schauder alternative, the lower and upper solution method and the monotone iterative technique.

Impulsive functional differential equations with variable times

In this note, a Schaefer fixed-point theorem is used to investigate the existence of solutions for first-order impulsive functional differential equations with variable times.

New maximum principles for first-order impulsive boundary value problems

In this paper, we establish new maximum principles for a boundary value problem for first-order impulsive differential equations.

Periodic boundary value problem for first-order impulsive ordinary differential equations

This paper investigates the existence of minimal and maximal solutions of the periodic boundary value problem for first-order impulsive differential equations by establishing two comparison results and using the method of upper and lower solutions and the monotone iterative technique.

Impulsive Semilinear Functional Differential Equations

In this paper the Leray–Schauder nonlinear alternative combined with semigroup theory is used to investigate the existence of mild solutions for first-order impulsive semilinear functional differential equations in Banach spaces.

Oscillation of Nonlinear Delay Impulsive Differential Equations and Inequalities

The oscillatory and asymptotic behavior of first-order nonlinear delay impulsive differential equations and inequalities is studied. Some new sharp sufficient conditions for oscillation and nonoscillation of solutions of the equations and inequalities are obtained. Many known results are improved. In particular, the conditions are necessary and sufficient if the equations and inequalities are autonomous.

Periodic boundary value problems for first-order impulsive ordinary differential equations

Periodic boundary value problems for first-order impulsive ordinary differential equations

Periodic boundary value problem for first-order impulsive functional differential equations

In this paper, by means of the method of upper and lower solutions and the monotone iterative technique, the existence of minimal and maximal solutions of the periodic boundary value problem for first-order impulsive functional differential equations is considered.

An existence result for first-order impulsive functional differential equations in banach spaces

In this paper, the Leray-Schauder nonlinear alternative is used to investigate the existence of solutions to first-order impulsive initial value problems for functional differential equations in Banach spaces.

Oscillation of first-order impulsive differential equations with advanced argument

For first-order linear impulsive differential equations with an advanced argument, various criteria for oscillation and nonoscillation of solutions of these equations are found. Some results of which improve the known theorems.

First-order impulsive ordinary differential equations with anti-periodic and nonlinear boundary conditions

The monotone iterative technique is a powerful method that have been used to approximate the extremal solutions of several problems [1, 2]. On the other hand, impulsive differential equations are a basic tool to study some problems of biology, medicine, engineering, and physics [3]. In this paper we deal with the following nonlinear boundary value problem for first order differential equation with impulses at fixed points

NONLINEAR DYNAMICS OF DRIVEN SINGLE-ELECTRON TUNNELING JUNCTIONS

In this paper we investigate the nonlinear dynamics of circuits made of single-electron tunneling junctions (SETJ) driven by a sinusoidal pump and biased by a DC voltage source. The mathematical model of an isolated SETJ circuit is a first-order nonautonomous impulsive differential equation. The tunneling effect of each SETJ can be realistically modeled by the impulsive effect of the junction voltage, which we choose to be the state variable of our circuit model. Based on this model we present theoretical results on the stability of the periodic and almost periodic solutions of driven SETJs. Our theoretical results show there are two phase states in each isolated SETJ circuit, which corresponds to two phase-shifted periodic solutions of our model. We present theoretical and numerical results of return maps of an isolated SETJ circuit. Our results also show that if the tunneling events are equipotentially almost periodic then the attractors generated by two-coupled SETJs will be confined to the vicinity of some periodic orbits. This result provides a foundation for implementing robust logic operations in nanoelectronics.