Global attractivity and positive almost periodic solution for delay logistic differential equation

2008 ◽  
Vol 68 (1) ◽  
pp. 54-72 ◽  
Author(s):  
Xitao Yang ◽  
Rong Yuan
Keyword(s):  
Differential Equation ◽  
Periodic Solution ◽  
Global Attractivity ◽  
Almost Periodic Solution ◽  
Almost Periodic ◽  
Positive Almost Periodic Solution

scholarly journals Positive Almost Periodic Solution on a Nonlinear Differential Equation

2011 ◽  
Vol 2011 ◽  
pp. 1-10 ◽  
Author(s):  
Ni Hua ◽  
Tian Li-xin ◽  
Liu Xun
Keyword(s):  
Differential Equation ◽  
Periodic Solution ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Nonlinear Equation ◽  
Sufficient Conditions ◽  
Almost Periodic Solution ◽  
Almost Periodic ◽  
Positive Almost Periodic Solution ◽  
The Stability

We study the following nonlinear equationdx(t)/dt=x(t)[a(t)-b(t)xα(t)-f(t,x(t))]+g(t), by using fixed point theorem, the sufficient conditions of the existence of a unique positive almost periodic solution for above system are obtained, by using the theories of stability, the sufficient conditions which guarantee the stability of the unique positive almost periodic solution are derived.

scholarly journals On the Stepanov-almost periodic solution of a second-order operator differential equation

1975 ◽  
Vol 19 (3) ◽  
pp. 261-263 ◽  
Author(s):  
Aribindi Satyanarayan Rao
Keyword(s):  
Differential Equation ◽  
Banach Space ◽  
Periodic Solution ◽  
Almost Periodic Solution ◽  
Second Order ◽  
Almost Periodicity ◽  
Operator Differential Equation ◽  
Almost Periodic ◽  
Order Operator ◽  
Image Position

Suppose X is a Banach space and J is the interval −∞<t<∞. For 1 ≦ p<∞, a function is said to be Stepanov-bounded or Sp-bounded on J if(for the definitions of almost periodicity and Sp-almost periodicity, see Amerio-Prouse (1, pp. 3 and 77).

scholarly journals On the Spectrum of almost periodic solutions of an abstract differential equation

1974 ◽  
Vol 18 (4) ◽  
pp. 385-387
Author(s):  
Aribindi Satyanarayan Rao ◽  
Walter Hengartner
Keyword(s):  
Differential Equation ◽  
Banach Space ◽  
Periodic Solution ◽  
Linear Operator ◽  
Periodic Function ◽  
Almost Periodic Solution ◽  
Almost Periodic Solutions ◽  
Almost Periodic Function ◽  
Almost Periodic ◽  
Abstract Differential Equation

AbstractIf a linear operator A in a Banach space satisfies certain conditions, then the spectrum of any almost periodic solution of the differential equation u′ = Au + f is shown to be identical with the spectrum of f, where f is a Stepanov almost periodic function.

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.

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