Existence and properties of an almost periodic solution to a system of nonlinear integrodifferential equations in Hilbert space in the neighborhood of an equilibrium point

1971 ◽  
Vol 22 (6) ◽  
pp. 720-722
Author(s):  
T. V. Melikidze
Keyword(s):  
Hilbert Space ◽  
Periodic Solution ◽  
Equilibrium Point ◽  
Almost Periodic Solution ◽  
Integrodifferential Equations ◽  
Almost Periodic

scholarly journals On the Almost Periodic Solutions of Differential Equations on Hilbert Spaces

2009 ◽  
Vol 2009 ◽  
pp. 1-11 ◽  
Author(s):  
Nguyen Thanh Lan
Keyword(s):  
Differential Equation ◽  
Hilbert Space ◽  
Periodic Solution ◽  
Periodic Solutions ◽  
Hilbert Spaces ◽  
Sufficient Conditions ◽  
Almost Periodic Solution ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Necessary And Sufficient

For the differential equation , on a Hilbert space , we find the necessary and sufficient conditions that the above-mentioned equation has a unique almost periodic solution. Some applications are also given.

scholarly journals Reducibility for a Class of Almost-Periodic Differential Equations with Degenerate Equilibrium Point under Small Almost-Periodic Perturbations

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Wenhua Qiu ◽  
Jianguo Si
Keyword(s):  
Differential Equation ◽  
Periodic Solution ◽  
Equilibrium Point ◽  
Almost Periodic Solution ◽  
Time Dependent ◽  
Almost Periodic ◽  
Degenerate Equilibrium ◽  
Periodic Transformation ◽  
Perturbed Equation ◽  
Kam Method

This paper focuses on almost-periodic time-dependent perturbations of an almost-periodic differential equation near the degenerate equilibrium point. Using the KAM method, the perturbed equation can be reduced to a suitable normal form with zero as equilibrium point by an affine almost-periodic transformation. Hence, for the equation we can obtain a small almost-periodic solution.

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.

Almost periodic solution to singular systems

1998 ◽  
Vol 43 (8) ◽  
pp. 698-700 ◽  
Author(s):  
Jiarong Liang ◽  
Yongqing Liu ◽  
Cunchen Gao
Keyword(s):  
Periodic Solution ◽  
Singular Systems ◽  
Almost Periodic Solution ◽  
Almost Periodic

Existence and exponential stability of almost periodic positive solution for host-macroparasite difference model

2016 ◽  
Vol 09 (02) ◽  
pp. 1650028
Author(s):  
Zhijian Yao
Keyword(s):  
Periodic Solution ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Exponential Stability ◽  
Positive Solution ◽  
Lyapunov Functional ◽  
Contraction Mapping ◽  
Almost Periodic Solution ◽  
Almost Periodic ◽  
Difference Model

This paper is concerned with a host-macroparasite difference model. By applying the contraction mapping fixed point theorem, we prove the existence of unique almost periodic positive solution. Moreover, we investigate the exponential stability of almost periodic solution by means of Lyapunov functional.

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