Existence, Uniqueness and Qualitative Properties of Global Solutions of Abstract Differential Equations with State-Dependent Delay

Hernández, Eduardo; Wu, Jianhong

doi:10.1017/s001309151800069x

Cited by 17 publications

(6 citation statements)

References 44 publications

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“…Combining ( 16) with (17), we obtain |z(t 1 )| 1 < M |ψ| 0 e −λt1 , which contradicts the equality (14). Hence, (13) holds.…”

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confidence: 85%

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Pseudo compact almost automorphy of neutral type Clifford-valued neural networks with mixed delays

2022

DCDS-B

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<p style='text-indent:20px;'>We consider a class of neutral type Clifford-valued cellular neural networks with discrete delays and infinitely distributed delays. Unlike most previous studies on Clifford-valued neural networks, we assume that the self feedback connection weights of the networks are Clifford numbers rather than real numbers. In order to study the existence of <inline-formula><tex-math id="M1">\begin{document}$ (\mu, \nu) $\end{document}</tex-math></inline-formula>-pseudo compact almost automorphic solutions of the networks, we prove a composition theorem of <inline-formula><tex-math id="M2">\begin{document}$ (\mu, \nu) $\end{document}</tex-math></inline-formula>-pseudo compact almost automorphic functions with varying deviating arguments. Based on this composition theorem and the fixed point theorem, we establish the existence and the uniqueness of <inline-formula><tex-math id="M3">\begin{document}$ (\mu, \nu) $\end{document}</tex-math></inline-formula>-pseudo compact almost automorphic solutions of the networks. Then, we investigate the global exponential stability of the solution by employing differential inequality techniques. Finally, we give an example to illustrate our theoretical finding. Our results obtained in this paper are completely new, even when the considered networks are degenerated into real-valued, complex-valued or quaternion-valued networks.</p>

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“…Combining ( 16) with (17), we obtain |z(t 1 )| 1 < M |ψ| 0 e −λt1 , which contradicts the equality (14). Hence, (13) holds.…”

mentioning

confidence: 85%

“…Also, all of these applications are closely related to their dynamics. However, there are few results about the dynamics of Clifford-valued neural networks [13][14][15][16][17][18][19]. In addition, Clifford-valued neural networks refer to the neural networks whose state variables, connection weights and external inputs are all Clifford numbers.…”

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confidence: 99%

Pseudo compact almost automorphy of neutral type Clifford-valued neural networks with mixed delays

2022

DCDS-B

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“…As a result, these equations have attracted a lot of attention (see for instance, [17][18][19][20][21][22][23]). In [24], the authors studied some local and global existence and uniqueness results for abstract diferential equations with state-dependent argument.…”

Section: Introductionmentioning

confidence: 99%

Approximate Controllability and Ulam Stability for Second-Order Impulsive Integrodifferential Evolution Equations with State-Dependent Delay

Bensalem,

Salim,

Benchohra

et al. 2024

International Journal of Differential Equations

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In this paper, we shall establish sufficient conditions for the existence, approximate controllability, and Ulam–Hyers–Rassias stability of solutions for impulsive integrodifferential equations of second order with state-dependent delay using the resolvent operator theory, the approximating technique, Picard operators, and the theory of fixed point with measures of noncompactness. An example is presented to illustrate the efficiency of the result obtained.

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“…Equations with state-dependent delays have piqued the interest of specialists because they have numerous application models, such as the two-body problem of classical electrodynamics, and they also have numerous applications within the class of problems with memories, such as in hereditary phenomena, see [42,43]. Several articles (see [1,18,30,31]) investigated this equation.…”

Section: Introductionmentioning

confidence: 99%

Existence and controllability results for an impulsive stochastic integro-differential equations with state-dependent delay

et al. 2023

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This study aims to investigate the existence of mild solutions for a class of impulsive stochastic integrodifferential equations with state-dependent delay in a real separable Hilbert space, as well as the controllability of these solutions. We offer Sufficient conditions for the existence and controllability results using the fixed point techniques combined with the theory of resolvent operator in Grimmer and analysis stochastic. Finally, we provide an example to illustrate the obtained results.

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Existence, Uniqueness and Qualitative Properties of Global Solutions of Abstract Differential Equations with State-Dependent Delay

Cited by 17 publications

References 44 publications

Pseudo compact almost automorphy of neutral type Clifford-valued neural networks with mixed delays

Pseudo compact almost automorphy of neutral type Clifford-valued neural networks with mixed delays

Approximate Controllability and Ulam Stability for Second-Order Impulsive Integrodifferential Evolution Equations with State-Dependent Delay

Existence and controllability results for an impulsive stochastic integro-differential equations with state-dependent delay

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