Existence and uniqueness of -almost periodic solutions to some ordinary differential equations

2007 ◽  
Vol 66 (9) ◽  
pp. 1899-1910 ◽  
Author(s):  
Jin Liang ◽  
L. Maniar ◽  
G.M. N’Guérékata ◽  
Ti-Jun Xiao
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Periodic Solutions ◽  
Existence And Uniqueness ◽  
Almost Periodic Solutions ◽  
Almost Periodic

scholarly journals Remotely Almost Periodic Solutions of Ordinary Differential Equations

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
C. Maulén ◽  
S. Castillo ◽  
M. Kostić ◽  
M. Pinto
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Periodic Solutions ◽  
Existence And Uniqueness ◽  
Exponential Dichotomy ◽  
Almost Periodicity ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Homogeneous Part

In this paper, we analyze the existence and uniqueness of remotely almost periodic solutions for systems of ordinary differential equations. The existence and uniqueness of remotely almost periodic solutions are achieved by using the results about the exponential dichotomy and the Bi-almost remotely almost periodicity of the homogeneous part of the corresponding systems of ordinary differential equations under our consideration.

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 Ergodicity and asymptotically almost periodic solutions of some differential equations

2001 ◽  
Vol 25 (12) ◽  
pp. 787-801 ◽  
Author(s):  
Chuanyi Zhang
Keyword(s):  
Periodic Solution ◽  
Differential Equations ◽  
Periodic Solutions ◽  
Existence And Uniqueness ◽  
Nonlinear Differential Equations ◽  
Almost Periodic Solution ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Ergodic Condition ◽  
Asymptotically Almost Periodic

Using ergodicity of functions, we prove the existence and uniqueness of (asymptotically) almost periodic solution for some nonlinear differential equations. As a consequence, we generalize a Massera’s result. A counterexample is given to show that the ergodic condition cannot be dropped.

scholarly journals Almost Periodic Solutions of First-Order Ordinary Differential Equations

Mathematics ◽  
2018 ◽  
Vol 6 (9) ◽  
pp. 171 ◽  
Author(s):  
Seifedine Kadry ◽  
Gennady Alferov ◽  
Gennady Ivanov ◽  
Artem Sharlay
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Periodic Solutions ◽  
Upper And Lower Bounds ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
First Order ◽  
Existence And Stability ◽  
Solutions Of Equations ◽  
The Right

Approaches to estimate the number of almost periodic solutions of ordinary differential equations are considered. Conditions that allow determination for both upper and lower bounds for these solutions are found. The existence and stability of almost periodic problems are studied. The novelty of this paper lies in the fact that the use of apparatus derivatives allows for the reduction of restrictions on the degree of smoothness of the right parts. In the works of Lebedeva [1], regarding the number of periodic solutions of equations first order, they required a high degree of smoothness. Franco et al. required the smoothness of the second derivative of the Schwartz equation [2]. We have all of these restrictions lifted. Our new form presented also emphasizes this novelty.

scholarly journals Mean Square Almost Periodic Solutions for Impulsive Stochastic Differential Equations with Delays

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Ruojun Zhang ◽  
Nan Ding ◽  
Linshan Wang
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Periodic Solutions ◽  
Existence And Uniqueness ◽  
Mean Square ◽  
Almost Periodic Solutions ◽  
Almost Periodic

We establish a result on existence and uniqueness on mean square almost periodic solutions for a class of impulsive stochastic differential equations with delays, which extends some earlier works reported in the literature.

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