Order Impulsive Differential Equations Research Articles

Asymptotic Behavior of <i>n</i>th Order Impulsive Differential Equations

This paper devotes to the asymptotic behavior of all solutions of nth order impulsive differential equations. Based on impulsive differential inequality, boundedness and zero tendency of every solution for nth order impulsive differential equations are obtained. In addition, we derive globally uniformly exponential stability of every solution under Lyapunov function and impulsivetechnique, and these results are extend to <i>n</i>th order differential equations with periodic coefficient and periodic impulse. Meanwhile, an example with simulations are provided to verify the conclusion.

The explicit solution of a class of higher order impulsive fractional differential equation involving Hadamard fractional derivative

In this paper, we obtain the explicit solution of a class of singular impulsive fractional differential equation of order [Formula: see text] involving the Hadamard fractional derivatives. In particular, the result is given in the form of necessary and sufficient conditions about the explicit solution. The proof of the main theorem is obtained by converting boundary value problems into integral equations and applying analytical techniques. Finally, some examples explain the application of the main theorem in this paper.

Wellposedness of impulsive functional abstract second-order differential equations with state-dependent delay

Abstract This study investigates the functional abstract second order impulsive differential equation with state-dependent delay. The major result of this study is that the abstract second-order impulsive differential equation with state-dependent delay system has at least one solution and is unique. After that, the wellposed condition is defined. Following that, we look at whether the proposed problem is wellposed. Finally, some illustrations of our findings are provided.

Stability Analysis of Second Order Impulsive Differential Equations

Stability Analysis of Second Order Impulsive Differential Equations

EXISTENCE AND UNIQUENESS OF DISCONTINUOUS PERIODIC ORBITS IN SECOND ORDER DIFFERENTIAL EQUATIONS WITH STATE-DEPENDENT IMPULSES

<abstract> In this paper, we are concerned with the existence and uniqueness of discontinuous periodic orbits for a class of second order impulsive differential equations with state-dependent jumps. we apply geometric method to estimate the time mapping of the equation, and then by using Poincaré-Bohl fixed point theorem to obtain some existence criteria under assumptions that the nonlinear term satisfies linear growth conditions. And, the uniqueness of the discontinuous periodic orbit is further proved. Finally, several specific impulsive functions are presented in examples to illustrate the obtained results. </abstract>

Positive solutions for second order impulsive differential equations with integral boundary conditions on an infinite interval

This paper is concerned with the existence of positive solutions of second-order impulsive differential equations with integral boundary conditions on an infinite interval. As an application, an example is given to demonstrate our main results.

Study of multi term delay fractional order impulsive differential equation using fixed point approach

&lt;abstract&gt;&lt;p&gt;This manuscript is devoted to investigate a class of multi terms delay fractional order impulsive differential equations. Our investigation includes existence theory along with Ulam type stability. By using classical fixed point theorems, we establish sufficient conditions for existence and uniqueness of solution to the proposed problem. We develop some appropriate conditions for different kinds of Ulam-Hyers stability results by using tools of nonlinear functional analysis. We demonstrate our results by an example.&lt;/p&gt;&lt;/abstract&gt;

Kamenev type oscillation criteria for second order impulsive differential equations

The oscillation of second order impulsive differential equations is discussed using Riccati transformations technique. New oscillation criteria are established, to improve and extend some recent results in the literature. Two illustrative examples are given.

Analysis on Controllability Results for Wellposedness of Impulsive Functional Abstract Second-Order Differential Equation with State-Dependent Delay

The functional abstract second order impulsive differential equation with state dependent delay is studied in this paper. First, we consider a second order system and use a control to determine the controllability result. Then, using Sadovskii’s fixed point theorem, we get sufficient conditions for the controllability of the proposed system in a Banach space. The major goal of this study is to demonstrate the controllability of an abstract second-order impulsive differential system with a state dependent delay mechanism. The wellposed condition is then defined. Next, we studied whether the defined problem is wellposed. Finally, we apply our results to examine the controllability of the second order state dependent delay impulsive equation.

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.

Semi-nonoscillation intervals and sign-constancy of Green’s functions of two-point impulsive boundary-value problems

UDC 517.9 We consider the second order impulsive differential equation with delays where for In this paper, we obtain the conditions of semi-nonoscillation for the corresponding homogeneous equation on the interval Using these results, we formulate theorems on sign-constancy of Green's functions for two-point impulsive boundary-value problems in terms of differential inequalities.

Dhage iteration principle for IVPs of nonlinear first order impulsive differential equations

In this paper we prove the existence and approximation theorems for the initial value problems of first order nonlinear impulsive differential equations under certain mixed partial Lipschitz and partial compactness type conditions. Our results are based on the Dhage monotone iteration principle embodied in a hybrid fixed point theorem of Dhage involving the sum of two monotone order preserving operators in a partially ordered Banach space. The novelty of the present approach lies the fact that we obtain an algorithm for the solution. Our abstract main result is also illustrated by indicating a numerical example.

RETRACTED: Existence of solutions for fractional order impulsive differential equations with integral boundary conditions

In this paper, we prove the expression and the existence of a class of nonlinear impulsive fractional order differential equations with integral boundary conditions. The unique solution of the differential equations by Green’s function is given. By using Schauder fixed point theorem and Leray-Schauder fixed point theorem, several sufficient conditions for the existence and uniqueness results are established.

Solutions to periodic BVP for second order impulsive differential equation with a p-Laplacian operator

Solutions to periodic BVP for second order impulsive differential equation with a p-Laplacian operator

Existence of positive solutions for second order impulsive differential equations with integral boundary conditions on the real line

This paper is denoted to study the existence of impulsive differential equations involving integral boundary conditions on the whole line by means of the Leray-Schauder Nonlinear Alternative theorem. An example is demonstrated the effectiveness of the our main result.

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.

CONTROLLABILITY AND HYERS—ULAM STABILITY OF IMPULSIVE SECOND ORDER ABSTRACT DAMPED DIFFERENTIAL SYSTEMS

<abstract> In this paper, we consider system of damped second order abstract impulsive differential equations to investigate its controllability and Hyers—Ulam stability. For our results about the controllability, we utilized the theory of strongly continuous cosine families of linear operators combined with Sadovskii fixed point theorem. In addition, different types of Hyers—Ulam stability is established with the help of Gr?nwall's type inequality and Lipschitz conditions. At last, we give an example of damped wave equation which outline the application of our principle results. </abstract>

Some Existence Results for High Order Fractional Impulsive Differential Equation on Infinite Interval

In this paper, we consider the high order impulsive differential equation on infinite interval D 0 + α u t + f t , u t , J 0 + β u t , D 0 + α − 1 u t = 0 , t ∈ 0 , ∞ ∖ t k k = 1 m △ u t k = I k u t k , t = t k , k = 1 , … , m u 0 = u ′ 0 = ⋯ = u n − 2 0 = 0 , D 0 + α − 1 u ∞ = u 0 By applying Schauder fixed points and Altman fixed points, we obtain some new results on the existence of solutions. The nonlinear term of the equation contains fractional integral operator J β u t and lower order derivative operator D 0 + α − 1 u t . An example is presented to illustrate our results.

Numerical approach to the controllability of fractional order impulsive differential equations

AbstractIn this manuscript, a numerical approach for the stronger concept of exact controllability (total controllability) is provided. The proposed control problem is a nonlinear fractional differential equation of order\alpha \in (1,2]with non-instantaneous impulses in finite-dimensional spaces. Furthermore, the numerical controllability of an integro-differential equation is briefly discussed. The tool for studying includes the Laplace transform, the Mittag-Leffler matrix function and the iterative scheme. Finally, a few numerical illustrations are provided through MATLAB graphs.

Oscillation Criteria for Solutions of Neutral Differential Equations of Impulses Effect with Positive and Negative Coefficients

In this paper, some necessary and sufficient conditions are obtained to ensure the oscillatory of all solutions of the first order impulsive neutral differential equations. Also, some results in the references have been improved and generalized. New lemmas are established to demonstrate the oscillation property. Special impulsive conditions associated with neutral differential equation are submitted. Some examples are given to illustrate the obtained results.