Order Impulsive Differential Research Articles

Existence and Uniqueness of Anti-Periodic Solution for Second Order Impulsive Differential Equations

In this article, we study the existence and uniqueness of anti-periodic solution to a second order impulsive differential equation as follows: where in the first argument and ϕ are ???? periodic, is a positive constant. By using the method of coincidence degree.

Stability Analysis of Second Order Impulsive Differential Equations

Stability Analysis of Second Order Impulsive Differential Equations

Variational Methods to the p-Laplacian type Nonlinear Fractional Order Impulsive Differential Equations with Sturm-Liouville Boundary-Value Problem

Abstract In this paper, we consider a class of nonlinear fractional impulsive differential equation involving Sturm-Liouville boundary-value conditions and p-Laplacian operator. By making use of critical point theorem and variational methods, some new criteria are given to guarantee that the considered problem has infinitely many solutions. Our results extend some recent results and the conditions of assumptions are easily verified. Finally, an example is given as an application of our fundamental results.

Multiplicity Results for Second Order Impulsive Differential Equations via Variational Methods

In this paper we investigate a class of impulsive differential equations with Dirichlet boundary conditions. Firstly, we define new inner product of and prove that the norm which is deduced by the inner product is equivalent to the usual norm. Secondly, we construct the lower and upper solutions of (1.1). Thirdly, we obtain the existence of a positive solution, a negative solution and a sign-changing solution by using critical point theory and variational methods. Finally, an example is presented to illustrate the application of our main result.

Criteria on Existence of Solutions for Fractional Order Impulsive Differential System with Infinite Delay

The paper is mainly concerned with the existence and uniqueness of solution for a class of Cauchy initial value problem of fractional order with impulses and infinite delay. The criteria on existences and uniqueness are obtained via successive approximation and solution operator. Finally an example is given to support our main result.

RETRACTION NOTICE TO “PERIODIC SOLUTIONS OF SECOND ORDER IMPULSIVE DIFFERENTIAL EQUATIONS AT RESONANCE VIA VARIATIONAL APPROACH” [MATH. MODEL. ANAL. 19(5):664–675, 2014

Retraction notice to “Periodic Solutions of Second Order Impulsive Differential Equations at Resonance via Variational Approach” [Math. Model. Anal. 19(5):664–675, 2014]

Numeric-analytic Solution to the Second Order Impulsive Differential Equations with Smooth Coefficients

In this paper a new method is proposed for finding series solution to the second orders impulsive differential equations with smooth coefficients. The method is applied to two examples using Maple 18 symbolic programming. A criterion for convergence of the series solution is obtained too.

Positive Solutions of Singular Dirichlet Boundary Value Problems for Second Order Impulsive Differential Equations

Positive Solutions of Singular Dirichlet Boundary Value Problems for Second Order Impulsive Differential Equations

Positive Solutions of Singular Periodic Boundary Value Problems for Second Order Impulsive Differential Equations

Positive Solutions of Singular Periodic Boundary Value Problems for Second Order Impulsive Differential Equations

Existence of Solution for Second Order Impulsive Differential Equations with Mixed Boundary Conditions

In this paper, we use variational methods to investigate the solutions of impulsive differential equations with mixed boundary conditions. The conditions for the existence of solution are established. The main results are also demonstrated with examples.

Existence and Uniqueness of Positive Solutions to Nonlinear Second Order Impulsive Differential Equations with Concave or Convex Nonlinearities

Using a new fixed point theorem of generalized concave operators, we present in this paper criteria which guarantee the existence and uniqueness of positive solutions to nonlinear two-point boundary value problems for second-order impulsive differential equations with concave or convex nonlinearities.

Optimal Control Problem of Positive Solutions to Second Order Impulsive Differential Equations

In this paper, we consider optimal control problem of second order impulsive differential equations. We show the existence and uniqueness of positive solutions to our problem for each given control functions. Also, we consider the control problem of positive solutions to our equations. Then, we prove the existence of an optimal control that minimizes the nonlinear cost functional. Moreover we give an example of the main results.

Positive Solutions of Multi-Point Boundary Value Problems for Second Order Impulsive Differential Equations with Deviating Arguments

In this article, we discuss the nonlinear multi-point boundary value problems for second order impulsive differential equations. Some sufficient conditions for the existence and nonexistence of positive solutions are proposed by using fixed point theorem in a cone.

Periodic Boundary Value Problems for the Second Order Impulsive Differential Equations

This paper is concerned with solutions of periodic boundary value problems for the second order impulsive differential equation. We prove the existence of extreme solutions and present the method of lower and upper solutions coupled with monotone iterative technique. Some comparison results are also established.

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.

Existence of Solutions of Boundary Value Problems for Nonlinear Second Order Impulsive Differential Equations in Banach Spaces

In this paper, the author uses the fixed point theory to investigate the existence of solutions of two-point boundary value problems for nonlinear second order impulsive differential equations in Banach spaces.