scholarly journals Existence and Uniqueness of Nontrivial Periodic Solutions to a Discrete Switching Model

Mathematics ◽  
2021 ◽  
Vol 9 (19) ◽  
pp. 2377
Author(s):  
Lijie Chang ◽  
Yantao Shi ◽  
Bo Zheng
Keyword(s):  
Periodic Solutions ◽  
Existence And Uniqueness ◽  
Sufficient Conditions ◽  
Wolbachia Infection ◽  
Switching Model ◽  
Switching Models ◽  
Nontrivial Periodic Solutions ◽  
Release Ratio ◽  
Release Method ◽  
Release Strategy

To control the spread of mosquito-borne diseases, one goal of the World Mosquito Program’s Wolbachia release method is to replace wild vector mosquitoes with Wolbachia-infected ones, whose capability of transmitting diseases has been greatly reduced owing to the Wolbachia infection. In this paper, we propose a discrete switching model which characterizes a release strategy including an impulsive and periodic release, where Wolbachia-infected males are released with the release ratio α1 during the first N generations, and the release ratio is α2 from the (N+1)-th generation to the T-th generation. Sufficient conditions on the release ratios α1 and α2 are obtained to guarantee the existence and uniqueness of nontrivial periodic solutions to the discrete switching model. We aim to provide new methods to count the exact numbers of periodic solutions to discrete switching models.

scholarly journals Eberlein weak almost periodic solutions for a class of integro-differential equations with infinite delay

2018 ◽  
Vol 5 (1) ◽  
pp. 127-137
Author(s):  
Khalil Ezzinbi ◽  
Samir Fatajou ◽  
Fatima Zohra Elamrani
Keyword(s):  
Differential Equations ◽  
Periodic Solutions ◽  
Banach Spaces ◽  
Existence And Uniqueness ◽  
Infinite Delay ◽  
Sufficient Conditions ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Weakly Almost Periodic

AbstractIn thiswork,we provide sufficient conditions ensuring the existence and uniqueness of an Eberlein weakly almost periodic solutions for some semilinear integro-differential equations with infinite delay in Banach spaces. For illustration, we provide an example arising in viscoelasticity theory.

scholarly journals Nontrivial periodic solutions to delay difference equations via Morse theory

2018 ◽  
Vol 16 (1) ◽  
pp. 885-896 ◽  
Author(s):  
Yuhua Long ◽  
Haiping Shi ◽  
Xiaoqing Deng
Keyword(s):  
Periodic Solutions ◽  
Difference Equations ◽  
Morse Theory ◽  
Sufficient Conditions ◽  
Asymptotically Linear ◽  
Linear Delay ◽  
Nontrivial Periodic Solutions ◽  
Delay Difference Equations ◽  
Delay Difference

AbstractIn this paper some sufficient conditions are obtained to guarantee the existence of nontrivial 4T + 2 periodic solutions of asymptotically linear delay difference equations. The approach used is based on Morse theory.

Almost Periodic Solutions of Monotone Second-Order Differential Equations

2011 ◽  
Vol 11 (3) ◽  
Author(s):  
Moez Ayachi ◽  
Joël Blot ◽  
Philippe Cieutat
Keyword(s):  
Differential Equation ◽  
Hilbert Space ◽  
Periodic Solution ◽  
Periodic Solutions ◽  
Existence And Uniqueness ◽  
Sufficient Conditions ◽  
Almost Periodic Solution ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Second Order Differential Equations

AbstractWe give sufficient conditions for the existence of almost periodic solutions of the secondorder differential equationu′′(t) = f (u(t)) + e(t)on a Hilbert space H, where the vector field f : H → H is monotone, continuous and the forcing term e : ℝ → H is almost periodic. Notably, we state a result of existence and uniqueness of the Besicovitch almost periodic solution, then we approximate this solution by a sequence of Bohr almost periodic solutions.

scholarly journals Periodic solutions for a model of tumor volume with anti-angiogenic periodic treatment

2021 ◽  
Vol 55 (1) ◽  
pp. 13-20
Author(s):  
Homero Díaz-Marín ◽  
Osvaldo Osuna
Keyword(s):  
Experimental Data ◽  
Periodic Solution ◽  
Numerical Simulations ◽  
Periodic Solutions ◽  
Existence And Uniqueness ◽  
Tumor Volume ◽  
Volume Growth ◽  
Sufficient Conditions ◽  
Cancer Tissue ◽  
Periodic Treatment

In this work, we consider the dynamics of a model for tumor volume growth under a drug periodic treatment targeting the process of angiogenesis within the vascularized cancer tissue. We give sufficient conditions for the existence and uniqueness of a global attractor consisting of a periodic solution. This conditions happen to be satisfied by values of the parameters tested for realistic experimental data. Numerical simulations are provided illustrating our findings.

On Periodic Solutions of Nonlinear Functional Differential Equations

1999 ◽  
Vol 6 (1) ◽  
pp. 45-64
Author(s):  
I. Kiguradze ◽  
B. Půža
Keyword(s):  
Differential Equation ◽  
Periodic Solution ◽  
Periodic Solutions ◽  
Existence And Uniqueness ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Continuous Operator ◽  
Nonlinear Functional ◽  
Continuous Vector ◽  
Functional Differential

Abstract Sufficient conditions are established for the existence and uniqueness of an ω-periodic solution of the functional differential equation where f is a continuous operator acting from the space of n-dimensional ω-periodic continuous vector functions into the space of n-dimensional ω-periodic and summable on [0, ω] vector functions.

scholarly journals Existence of Coupled Best Proximity Points of p-Cyclic Contractions

Axioms ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 39
Author(s):  
Miroslav Hristov ◽  
Atanas Ilchev ◽  
Diana Nedelcheva ◽  
Boyan Zlatanov
Keyword(s):  
Wide Class ◽  
Existence And Uniqueness ◽  
Sufficient Conditions ◽  
Best Proximity Points ◽  
Cyclic Contractions ◽  
Ordered Pairs

We generalize the notion of coupled fixed (or best proximity) points for cyclic ordered pairs of maps to p-cyclic ordered pairs of maps. We find sufficient conditions for the existence and uniqueness of the coupled fixed (or best proximity) points. We illustrate the results with an example that covers a wide class of maps.

scholarly journals Correctness conditions for high-order differential equations with unbounded coefficients

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Kordan N. Ospanov
Keyword(s):  
Differential Equation ◽  
Hilbert Space ◽  
Existence And Uniqueness ◽  
Sufficient Conditions ◽  
Integral Operators ◽  
Order Linear Differential Equation ◽  
Unbounded Coefficients ◽  
Weighted Norms ◽  
Uniqueness Of The Solution ◽  
Linear Differential

AbstractWe give some sufficient conditions for the existence and uniqueness of the solution of a higher-order linear differential equation with unbounded coefficients in the Hilbert space. We obtain some estimates for the weighted norms of the solution and its derivatives. Using these estimates, we show the conditions for the compactness of some integral operators associated with the resolvent.

scholarly journals Horosphere slab separation theorems in manifolds without conjugate points

2019 ◽  
Vol 27 (1) ◽  
Author(s):  
Sameh Shenawy
Keyword(s):  
Euclidean Space ◽  
Hyperbolic Space ◽  
Existence And Uniqueness ◽  
Convex Set ◽  
Sufficient Conditions ◽  
Conjugate Points ◽  
Separation Theorems ◽  
Farthest Points ◽  
Simply Connected ◽  
Convex Subsets

Abstract Let $\mathcal {W}^{n}$ W n be the set of smooth complete simply connected n-dimensional manifolds without conjugate points. The Euclidean space and the hyperbolic space are examples of these manifolds. Let $W\in \mathcal {W}^{n}$ W ∈ W n and let A and B be two convex subsets of W. This note aims to investigate separation and slab horosphere separation of A and B. For example,sufficient conditions on A and B to be separated by a slab of horospheres are obtained. Existence and uniqueness of foot points and farthest points of a convex set A in $W\in \mathcal {W}$ W ∈ W are considered.

scholarly journals On the equivalence of three-dimensional differential systems

2020 ◽  
Vol 18 (1) ◽  
pp. 1164-1172
Author(s):  
Jian Zhou ◽  
Shiyin Zhao
Keyword(s):  
Periodic Solutions ◽  
Differential System ◽  
Necessary Conditions ◽  
Three Dimensional ◽  
Sufficient Conditions ◽  
Periodic Systems ◽  
Structural Form ◽  
Differential Systems

Abstract In this paper, firstly, we study the structural form of reflective integral for a given system. Then the sufficient conditions are obtained to ensure there exists the reflective integral with these structured form for such system. Secondly, we discuss the necessary conditions for the equivalence of such systems and a general three-dimensional differential system. And then, we apply the obtained results to the study of the behavior of their periodic solutions when such systems are periodic systems in t.

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