ON A QUASI‐ISOMETRY FOR QUASICONFORMAL MAPPING SATISFYING POISSON DIFFERENTIAL INEQUALITY

Mathematika ◽  
2020 ◽  
Vol 67 (1) ◽  
pp. 61-70
Author(s):  
Deguang Zhong
Keyword(s):  
Quasiconformal Mapping ◽  
Differential Inequality

scholarly journals Functional Differential Inequalities with Unbounded Delay

2005 ◽  
Vol 12 (2) ◽  
pp. 237-254
Author(s):  
Zdzisław Kamont ◽  
Adam Nadolski
Keyword(s):  
Differential Inequality ◽  
Continuous Dependence ◽  
Functional Differential Equations ◽  
Uniqueness Result ◽  
Classical Solutions ◽  
Differential Inequalities ◽  
Unbounded Delay ◽  
Several Variables ◽  
Functional Differential ◽  
Continuous Dependence Of Solutions

Abstract We prove that a function of several variables satisfying a functional differential inequality with unbounded delay can be estimated by a solution of a suitable initial problem for an ordinary functional differential equation. As a consequence of the comparison theorem we obtain a Perron-type uniqueness result and a result on continuous dependence of solutions on given functions for partial functional differential equations with unbounded delay. We consider classical solutions on the Haar pyramid.

scholarly journals Uniform persistence and almost periodic solutions of a nonautonomous patch occupancy model

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Hui Zhou ◽  
Jehad Alzabut ◽  
Shahram Rezapour ◽  
Mohammad Esmael Samei
Keyword(s):  
Differential Inequality ◽  
Almost Periodic Solution ◽  
Rocky Intertidal ◽  
Uniform Persistence ◽  
Almost Periodic ◽  
Patch Occupancy ◽  
Sharp Threshold ◽  
Intertidal Community ◽  
Patch Occupancy Model ◽  
Inequality Techniques

Abstract In this paper, a nonlinear nonautonomous model in a rocky intertidal community is studied. The model is composed of two species in a rocky intertidal community and describes a patch occupancy with global dispersal of propagules and occupy each other by individual organisms. Firstly, we study the uniform persistence of the model via differential inequality techniques. Furthermore, a sharp threshold of global asymptotic stability and the existence of a unique almost periodic solution are derived. To prove the main results, we construct an appropriate Lyapunov function whose conditions are easily verified. The assumptions of the model are reasonable, and the results complement previously known ones. An example with specific values of parameters is included for demonstration of theoretical outcomes.

scholarly journals Existence and exponential stability of a periodic solution for fuzzy cellular neural networks with time-varying delays

2011 ◽  
Vol 21 (4) ◽  
pp. 649-658 ◽  
Author(s):  
Qianhong Zhang ◽  
Lihui Yang ◽  
Daixi Liao
Keyword(s):  
Neural Networks ◽  
Periodic Solution ◽  
Exponential Stability ◽  
Differential Inequality ◽  
Sufficient Conditions ◽  
Coincidence Degree ◽  
Cellular Neural Networks ◽  
Time Varying ◽  
Fuzzy Cellular Neural Networks ◽  
Inequality Technique

Existence and exponential stability of a periodic solution for fuzzy cellular neural networks with time-varying delays Fuzzy cellular neural networks with time-varying delays are considered. Some sufficient conditions for the existence and exponential stability of periodic solutions are obtained by using the continuation theorem based on the coincidence degree and the differential inequality technique. The sufficient conditions are easy to use in pattern recognition and automatic control. Finally, an example is given to show the feasibility and effectiveness of our methods.

Neural Networks L2-Gain Controller Design for Nonlinear System

2011 ◽  
Vol 467-469 ◽  
pp. 1505-1510
Author(s):  
Dan Liu ◽  
Ni Hong Wang ◽  
Gui Ying Li
Keyword(s):  
Neural Network ◽  
Disturbance Rejection ◽  
Differential Inequality ◽  
Controller Design ◽  
Design Method ◽  
General Structure ◽  
The Neural Network ◽  
Network Weight ◽  
Finite Gain ◽  
L2 Gain

This paper proposes a new method that it uses the neural network to construct the solution of the Hamiltion-Jacobi inequality (HJ), and it carries on the optimization of the neural network weight using the genetic algorithm. This method causes the Lyapunov function to satisfy the HJ, avoides solving the HJ parital differential inequality, and overcomes the difficulty which the HJ parital differential inequality analysis. Beside this, it proposes a design method of a nonlinear state feedback L2-gain disturbance rejection controller based on HJ, and introduces general structure of L2-gain disturbance rejection controller in the form of neural network. The simulation demonstrates the design of controller is feasible and the closed-loop system ensures a finite gain between the disturbance and the output.

scholarly journals On a Differential Equation Involving Hilfer-Hadamard Fractional Derivative

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
M. D. Qassim ◽  
K. M. Furati ◽  
N.-E. Tatar
Keyword(s):  
Differential Equation ◽  
Fractional Derivative ◽  
Global Solution ◽  
Differential Inequality ◽  
Source Term ◽  
Existence Of Solutions ◽  
Hadamard Fractional Derivative ◽  
Fractional Differential

This paper studies a fractional differential inequality involving a new fractional derivative (Hilfer-Hadamard type) with a polynomial source term. We obtain an exponent for which there does not exist any global solution for the problem. We also provide an example to show the existence of solutions in a wider space for some exponents.

scholarly journals Global Exponential Stability of Almost Periodic Solutions for SICNNs with Continuously Distributed Leakage Delays

2013 ◽  
Vol 2013 ◽  
pp. 1-14 ◽  
Author(s):  
Hong Zhang ◽  
Mingquan Yang
Keyword(s):  
Exponential Stability ◽  
Periodic Solutions ◽  
Differential Inequality ◽  
Sufficient Conditions ◽  
Functional Method ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Leakage Delays ◽  
Lyapunov Functional Method ◽  
Inequality Techniques

Shunting inhibitory cellular neural networks (SICNNs) are considered with the introduction of continuously distributed delays in the leakage (or forgetting) terms. By using the Lyapunov functional method and differential inequality techniques, some sufficient conditions for the existence and exponential stability of almost periodic solutions are established. Our results complement with some recent ones.

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