Sturm-Picone comparison theorems for nonlinear impulsive differential equations with discontinuous solutions
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DOI: 10.1002/mma.4571
Abstract: The nonlinear versions of Sturm-Picone comparison theorem as well as Leighton's variational lemma and Leighton's theorem for regular and singular nonlinear impulsive differential equations with discontinuous solutions having fixed moments of impulse actions are established.… read more here.
Keywords: sturm picone; nonlinear impulsive; impulsive differential; differential equations ... See more keywords
Nonlinear second-order impulsive differential problems with dependence on the derivative via variational structure
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DOI: 10.1007/s11784-019-0754-3
Abstract: In this paper we use variational methods and fixed point theorems to study the existence of solutions to a boundary value problem for impulsive differential equations with nonlinear dependence on the derivative. read more here.
Keywords: impulsive differential; second order; differential problems; dependence derivative ... See more keywords
Affine-Periodic Solutions for Impulsive Differential Systems
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DOI: 10.1007/s12346-019-00337-5
Abstract: The affine-periodicity is a new periodic concept which has been founded in recent years. In this paper, we will discuss the existence of affine-periodic solutions for impulsive differential systems. Several existence theorems are proved for… read more here.
Keywords: impulsive differential; periodic solutions; differential systems; systems affine ... See more keywords
Convergence Analysis for Iterative Learning Control of Conformable Impulsive Differential Equations
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DOI: 10.1007/s41980-020-00510-6
Abstract: This paper deals with iterative learning control for conformable impulsive differential equations. For nonlinear and linear problems varying with the initial state, we design standard P -type, $$D_{\gamma }$$ D γ -type, and conformable $$PI_{\gamma… read more here.
Keywords: impulsive differential; learning control; conformable impulsive; differential equations ... See more keywords
Stability of nonlinear variable-time impulsive differential systems with delayed impulses
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DOI: 10.1016/j.nahs.2020.100970
Abstract: Abstract This paper investigates the stability of nonlinear variable-time impulsive differential systems with delayed impulses. By using the comparison principle, the Lyapunov method and inequality techniques, some sufficient conditions for quasi-uniformly asymptotic stability and quasi-exponential… read more here.
Keywords: differential systems; impulsive differential; time impulsive; variable time ... See more keywords
hp-Legendre–Gauss collocation method for impulsive differential equations
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DOI: 10.1080/00207160.2015.1099632
Abstract: ABSTRACT The original Legendre–Gauss collocation method is derived for impulsive differential equations, and the convergence is analysed. Then a new hp-Legendre–Gauss collocation method is presented for impulsive differential equations, and the convergence for the hp-version… read more here.
Keywords: impulsive differential; legendre gauss; method; gauss collocation ... See more keywords
Randomized Sharkovsky-type theorems and their application to random impulsive differential equations and inclusions on tori
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DOI: 10.1142/s0219493719500369
Abstract: Our randomized versions of the Sharkovsky-type cycle coexistence theorems on tori and, in particular, on the circle are applied to random impulsive differential equations and inclusions. The obtained effective coexistence criteria for random subharmonics with… read more here.
Keywords: random impulsive; sharkovsky type; impulsive differential; equations inclusions ... See more keywords
Existence Theorem for Impulsive Differential Equations with Measurable Right Side for Handling Delay Problems
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DOI: 10.1155/2020/7089313
Abstract: Due to noncontinuous solution, impulsive differential equations with delay may have a measurable right side and not a continuous one. In order to support handling impulsive differential equations with delay like in other chapters of… read more here.
Keywords: impulsive differential; delay; right side; differential equations ... See more keywords
Stability and H∞ performance analysis for a class of impulsive differential systems
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DOI: 10.1177/0142331217741956
Abstract: The stability and H ∞ performance analysis of a class of impulsive differential systems are addressed by using a two-point boundary value problem method. For convenience of computation, a sufficient and necessary condition for the… read more here.
Keywords: performance analysis; impulsive differential; differential systems; class impulsive ... See more keywords
Nontrivial convex solutions on a parameter of impulsive differential equation with Monge-Ampère operator
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DOI: 10.1186/s13661-017-0904-8
Abstract: AbstractThe authors consider the impulsive differential equation with Monge-Ampère operator in the form of {((u′(t))n)′=λntn−1f(−u(t)),t∈(0,1),t≠tk,k=1,2,…,m,Δ(u′)n|t=tk=λIk(−u(tk)),k=1,2,…,m,u′(0)=0,u(1)=0,$$\textstyle\begin{cases} ( (u'(t) )^{n} )'=\lambda nt^{n-1}f (-u(t) ), \quad t\in(0,1), t\neq t_{k}, k=1, 2, \ldots, m, \\ \Delta (u' )^{n}|_{t=t_{k}}=\lambda I_{k}… read more here.
Keywords: differential equation; amp operator; impulsive differential; monge amp ... See more keywords
Razumikhin-type theorems for impulsive differential equations with piecewise constant argument of generalized type
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DOI: 10.1186/s13662-018-1725-5
Abstract: In this paper, we focus on developing Razumikhin technique for stability analysis of impulsive differential equations with piecewise constant argument. Based on the Lyapunov–Razumikhin method and impulsive control theory, we obtain some Razumikhin-type theorems on… read more here.
Keywords: piecewise constant; impulsive differential; constant argument; differential equations ... See more keywords