scholarly journals Weighted Pseudo Almost Periodic Solution to Partial Stochastic Neutral Evolution Equations

2022 ◽  
Keyword(s):  
Periodic Solution ◽  
Evolution Equations ◽  
Almost Periodic Solution ◽  
Neutral Evolution ◽  
Almost Periodic ◽  
Pseudo Almost Periodic Solution ◽  
Pseudo Almost Periodic

scholarly journals Asymptotic Behavior of Solution for Functional Evolution Equations with Stepanov Forcing Terms

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Zhong-Hua Wu
Keyword(s):  
Periodic Solution ◽  
Contraction Mapping ◽  
Evolution Equations ◽  
Measure Theory ◽  
Contraction Mapping Principle ◽  
Almost Periodic Solution ◽  
Almost Periodic ◽  
Functional Evolution ◽  
Pseudo Almost Periodic Solution ◽  
Pseudo Almost Periodic

Through the use of the measure theory, evolution family, “Acquistapace–Terreni” condition, and Hölder inequality, the core objective of this work is to seek to analyze whether there is unique μ -pseudo almost periodic solution to a functional evolution equation with Stepanov forcing terms in a Banach space. Certain adequate conditions are derived guaranteeing there is unique μ -pseudo almost periodic solution to the equation by Lipschitz condition and contraction mapping principle. Finally, an example is used to demonstrate our theoretical findings.

scholarly journals Pseudo Almost-Periodic Solution of Shunting Inhibitory Cellular Neural Networks with Delay

2011 ◽  
Vol 2011 ◽  
pp. 1-14 ◽  
Author(s):  
Haihui Wu
Keyword(s):  
Neural Networks ◽  
Periodic Solution ◽  
Cellular Neural Networks ◽  
Contraction Mapping Principle ◽  
Almost Periodic Solution ◽  
Almost Periodic ◽  
Pseudo Almost Periodic Solution ◽  
Globally Exponential Stability ◽  
Banach Contraction ◽  
Pseudo Almost Periodic

Shunting inhibitory cellular neural networks are studied. Some sufficient criteria are obtained for the existence and uniqueness of pseudo almost-periodic solution of this system. Our results improve and generalize those of the previous studies. This is the first paper considering the pseudo almost-periodic SICNNs. Furthermore, several methods are applied to establish sufficient criteria for the globally exponential stability of this system. The approaches are based on constructing suitable Lyapunov functionals and the well-known Banach contraction mapping principle.

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