Order Impulsive Differential Equations Research Articles

Positive periodic solutions for second order differential equations with impulsive effects

The existence of positive periodic solutions for a class of second order impulsive differential equations is studied. By using a fixed point theorem in cone, we obtain two existence results, which extend some known results.

New existence results for periodic boundary value problems with impulsive effects

New results as regards the existence of positive solutions for first order impulsive differential equations are provided. The method of proof relies on the fixed point theorem and degree theory. Some examples are presented to illustrate the main results.

Existence of solution for impulsive differential equations with indefinite linear part

In this paper, we consider the existence of solutions for second order impulsive differential equations with Dirichlet boundary conditions and indefinite linear part. An existence result is obtained by using Saddle point theorem, which extends and complements some existing results.

Impulsive boundary value problem with parameter

Abstract In this work, we investigate the existence of solutions for a class of second order impulsive differential equations using either the implicit function theorem or bifurcation techniques by the mean of Krasnosel'ski theorem.

Existence of solutions for the integral boundary value problems of fractional order impulsive differential equations

In this paper, we study a class of integral boundary value problem for fractional order impulsive differential equations, where both the nonlinearity and the impulsive terms contain the fractional order derivatives. By using fixed-point theorems, the existence results of solution for the boundary value problem are established. Finally, some examples are presented to illustrate the existence results. Copyright © 2015 John Wiley & Sons, Ltd.

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]

Existence of eventually positive solutions of higher order impulsive delay differential equations

A search of the literature reveals only a few studies on the necessary as well as sufficient conditions for the existence of eventually positive and/or monotone solutions of higher order impulsive differential equations that also allow delays. To fill this gap, we study a general class of higher order impulsive delay differential equations and establish necessary and/or sufficient conditions for the existence of eventually positive and monotone solutions. Our results are sharp in the sense that, in special cases, they are necessary and sufficient. Illustrative examples are included.

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.

Lazer-Leach type condition for second order differential equations at resonance with impulsive effects via variational method

In this paper, we study the existence of periodic solutions of second order impulsive differential equations at resonance with impulsive effects. We prove the existence of periodic solutions under a generalized Lazer-Leach type condition by using variational method. The impulses can generate a periodic solution.

Transformation techniques and fixed point theories to establish the positive solutions of second order impulsive differential equations

Using a new method for dealing with the impulse term of second impulsive differential equations, we are concerned with determining values of λ, for which there exist positive solutions of the following boundary value problems in the form of {λx″(t)+f(t,x(t))=0,t∈J,t≠tk,x(tk+)−x(tk)=ckx(tk),k=1,2,…,n,ax(0)−bx′(0)=ax(1)−bx′(1)=∫01h(s)x(t)dt, where λ>0 is a positive parameter, {ck} is a real sequence with ck>−1,k=1,2,…,n. The dependence of positive solution xλ(t) on the parameter λ is also studied, i.e., limλ→+∞‖xλ‖=+∞orlimλ→+∞‖xλ‖=0. The proof of our main result is based upon transformation techniques and fixed point theories. This is probably the first time the existence of positive solutions of second order impulsive differential equations has been studied by applying this technique.

Green’s function for Sturm-Liouville-type boundary value problems of fractional order impulsive differential equations and its application

In this paper, we discuss the expression and properties of Green’s function for boundary value problems of nonlinear Sturm-Liouville-type fractional order impulsive differential equations. Its applications are also given. Our results are compared with some recent results by Bai and Lu.

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

POSITIVE SOLUTIONS OF STURM-LIOUVILLE BVP FOR IMPULSIVE DIFFERENTIAL EQUATIONS WITH A NON-WELL-ORDERED UPPER AND LOWER SOLUTION CONDITION

In this paper,we consider the positive solution for Sturm-Liouville BVP of second order impulsive differential equations by using the fixed point index method under a non-well-ordered upper and lower solution condition.We prove the existence of positive solution of the impulsive boundary value problem.

Positive Solutions for Impulsive Differential Equations with Mixed Monotonicity and Optimal Control

We consider positive solutions and optimal control problem for a second order impulsive differential equation with mixed monotone terms. Firstly, by using a fixed point theorem of mixed monotone operator, we study positive solutions of the boundary value problem for impulsive differential equations with mixed monotone terms, and sufficient conditions for existence and uniqueness of positive solutions will be established. Also, we study positive solutions of the initial value problem for our system. Moreover, we investigate the control problem of positive solutions to our equations, and then, we prove the existence of an optimal control and its stability. In addition, related examples will be given for illustrations.

Existence and controllability results for damped second order impulsive functional differential systems with state-dependent delay

In this paper, we investigate the existence and controllability of mild solutions for a damped second order impulsive functional differential equation with state-dependent delay in Banach spaces. The results are obtained by using Sadovskii's fixed point theorem combined with the theories of a strongly continuous cosine family of bounded linear operators. Finally, an example is provided to illustrate the main results.

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.

The existence of solutions of periodic BVP for second order impulsive differential equations

In this paper, we study the existence of solutions of periodic boundary value problems for impulsive differential equations depending on a parameter λ. By employing an existing critical point theorem, we find the range of the control parameter in which the boundary value problem admits at least one non-zero weak solution. An example illustrates our results. MSC:34B15, 34B18, 34B37, 58E30.

Studies on anti‐periodic boundary value problems for two classes of special second order impulsive differential equations

We consider anti‐periodic boundary value problems for two classes of special second order impulsive differential equations. On the basis of several important impulsive differential inequalities, by using the monotone iterative technique coupled with lower and upper solutions, we obtain sufficient conditions to guarantee the existence and uniqueness of solutions for such problems. Further, we give two examples to illustrate our conclusions. Copyright © 2013 John Wiley & Sons, Ltd.

OSCILLATIONS OF OF FIRST ORDER IMPULSIVE DIFFERENTIAL NEUTRAL CONSTANT DELAY EQUATIONS WITH MIXED COEFFICIENTS

In this paper we consider first order impulsive neutral differential equation with constant delay, constant coefficient into the neutral term and variable coefficient into the rest. The asymptotic behavior of a non-oscillatory solution for such equations is investigated and sufficient conditions for oscilla- tion of all the solutions are found.