Partial dynamic equations on time scales

In this paper, based on the concept and properties of almost-complete closedness time scales (ACCTS), we investigate the existence of weighted pseudo double-almost periodic mild solutions for non-autonomous impulsive evolution equations. We also consider the exponential stability of weighted pseudo double-almost periodic solutions. Finally, we conclude our paper by providing several illustrative applications to different types of dynamic equations and mathematical models. These applications justify the practical usefulness of the established theoretical results.

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“…It follows from the same discussion as in Section 3.1 of [19] that the evolution system {T (t, s) : t s} satisfies T (t, s) e 1 2 (t, s) (t s)…”

Section: Theorem 316 Assume the Following Conditions Holdmentioning

confidence: 91%

Weighted piecewise pseudo double-almost periodic solution for impulsive evolution equations

Wang¹,

Agarwal²,

O’Regan³

2017

J. Nonlinear Sci. Appl.

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“…(1.1) can be found in the literature (see [3,11,12,26]). Moreover, the lack of suitable mathematical tools is in contrast with the use of (1.1) in applications: …”

Section: Introductionmentioning

confidence: 97%

Dynamic diffusion-type equations on discrete-space domains

Slavík

Stehlı́k

2015

Journal of Mathematical Analysis and Applications

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We consider a class of partial dynamic equations on discrete-space domains which includes, as a special case, the discrete-space versions of the diffusion (heat) equation. We focus on initial-value problems and study the existence and uniqueness of forward and backward solutions. Moreover, we discuss other topics such as sum and sign preservation, maximum and minimum principles, or symmetry of solutions.

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“…Therefore, many authors have studied the dynamical behaviors of neural networks on time scales for recent years (see Ref. [9][10][11][12][13][16][17] and reference therein).…”

Section: Introductionmentioning

confidence: 99%

Existence and Exponential Stability of Almost Periodic Solutions for Impulsive BAM Neural Networks on Almost Periodic Time Scales

Chen¹,

Xu²

2017

dtcse

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This paper considers almost periodic dynamics for impulsive BAM neural networks with variable delays and continuously distributed delays on almost periodic time scales. By applying contraction principle and Gromwell-Bellman's inequality, some new results on the existence and exponential stability of almost periodic solutions are established. In addition, an example is provided to illustrate the feasibility and effectiveness of the obtained results.

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Partial dynamic equations on time scales

Cited by 59 publications

References 3 publications

Weighted piecewise pseudo double-almost periodic solution for impulsive evolution equations

Weighted piecewise pseudo double-almost periodic solution for impulsive evolution equations

Dynamic diffusion-type equations on discrete-space domains

Existence and Exponential Stability of Almost Periodic Solutions for Impulsive BAM Neural Networks on Almost Periodic Time Scales

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