Boundedness, periodicity, and conditional stability of noninstantaneous impulsive evolution equations

Peng, Yang; Wang, JinRong; Fečkan, Michal

doi:10.1002/mma.6332

Cited by 13 publications

(7 citation statements)

References 30 publications

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“…Impulsive effects begin at any arbitrary fixed point and continue with a finite time interval, known as non-instantaneous impulses. For more details, we refer the reader to [15][16][17][18][19][20][21][22][23].…”

Section: Introductionmentioning

confidence: 99%

Approximate Controllability of Delayed Fractional Stochastic Differential Systems with Mixed Noise and Impulsive Effects

et al. 2023

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We herein report a new class of impulsive fractional stochastic differential systems driven by mixed fractional Brownian motions with infinite delay and Hurst parameter H^∈(1/2,1). Using fixed point techniques, a q-resolvent family, and fractional calculus, we discuss the existence of a piecewise continuous mild solution for the proposed system. Moreover, under appropriate conditions, we investigate the approximate controllability of the considered system. Finally, the main results are demonstrated with an illustrative example.

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Section: Introductionmentioning

confidence: 99%

Approximate Controllability of Delayed Fractional Stochastic Differential Systems with Mixed Noise and Impulsive Effects

et al. 2023

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“…In real life, many problems are represented by partial differential equations (PDEs), such as the advection-diffusion equation, the wave equation, and the Klein-Gordon equation. So, solving the partial differential equations [1][2][3][4] is of great practical significance. Traditional numerical methods: finite volume [5], finite element [6], and finite difference [7] have been very mature in solving partial differential equations.…”

Section: Introductionmentioning

confidence: 99%

M-WDRNNs: Mixed-Weighted Deep Residual Neural Networks for Forward and Inverse PDE Problems

Zheng,

Yang

2023

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Physics-informed neural networks (PINNs) have been widely used to solve partial differential equations in recent years. But studies have shown that there is a gradient pathology in PINNs. That is, there is an imbalance gradient problem in each regularization term during back-propagation, which makes it difficult for neural network models to accurately approximate partial differential equations. Based on the depth-weighted residual neural network and neural attention mechanism, we propose a new mixed-weighted residual block in which the weighted coefficients are chosen autonomously by the optimization algorithm, and one of the transformer networks is replaced by a skip connection. Finally, we test our algorithms with some partial differential equations, such as the non-homogeneous Klein–Gordon equation, the (1+1) advection–diffusion equation, and the Helmholtz equation. Experimental results show that the proposed algorithm significantly improves the numerical accuracy.

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“…Hernández [39] studied a general class of non-instantaneous abstract impulsive problem ‘without predefined times of impulse’. More recently, stability and robustness for non-instantaneous IDEs were given in Wang et al [40–42] and Yang et al [43]. The existence of an inertial manifold for semilinear non-instantaneous parabolic IDEs was given in Yang et al [44].…”

Section: Introductionmentioning

confidence: 99%

Smooth stable manifolds for the non-instantaneous impulsive equations with applications to Duffing oscillators

Pinto

Xia

2022

Proc. R. Soc. A.

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In this paper, we present a theory of smooth stable manifold for the non-instantaneous impulsive differential equations on the Banach space or Hilbert space. Assume that the non-instantaneous linear impulsive evolution differential equation admits a uniform exponential dichotomy, we give the conditions of the existence of the global and local stable manifolds. Furthermore, C k -smoothness of the stable manifold is obtained, and the periodicity of the stable manifold is given. Finally, an application to nonlinear Duffing oscillators with non-instantaneous impulsive effects is given, to demonstrate the existence of stable manifold.

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Boundedness, periodicity, and conditional stability of noninstantaneous impulsive evolution equations

Cited by 13 publications

References 30 publications

Approximate Controllability of Delayed Fractional Stochastic Differential Systems with Mixed Noise and Impulsive Effects

Approximate Controllability of Delayed Fractional Stochastic Differential Systems with Mixed Noise and Impulsive Effects

M-WDRNNs: Mixed-Weighted Deep Residual Neural Networks for Forward and Inverse PDE Problems

Smooth stable manifolds for the non-instantaneous impulsive equations with applications to Duffing oscillators

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