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.

On the almost periodic solution of an abstract diffferential equation

1974 ◽  
Vol 18 (2) ◽  
pp. 252-256
Author(s):  
Aribindi Satyanarayan Rao
Keyword(s):  
Differential Equation ◽  
Periodic Solution ◽  
Periodic Function ◽  
Bounded Solution ◽  
Almost Periodic Solution ◽  
Almost Periodic Function ◽  
Almost Periodic ◽  
Abstract Differential Equation ◽  
Weakly Almost Periodic

Abstract: Under certain suitable conditions, the Stepanov-bounded solution of an abstract differential equation corresponding to a Stepanov almost periodic function is strongly (weakly) almost periodic.

scholarly journals On the spectrum of weakly almost periodic solutions of certain abstract differential equations

1985 ◽  
Vol 8 (1) ◽  
pp. 109-112 ◽  
Author(s):  
Aribindi Satyanarayan Rao ◽  
L. S. Dube
Keyword(s):  
Differential Equation ◽  
Banach Space ◽  
Periodic Solution ◽  
Almost Periodic Solution ◽  
Almost Periodic Solutions ◽  
Almost Periodic Function ◽  
Dual Operator ◽  
Almost Periodic ◽  
Abstract Differential Equations ◽  
Weakly Almost Periodic

In a sequentially weakly complete Banach space, if the dual operator of a linear operatorAsatisfies certain conditions, then the spectrum of any weakly almost periodic solution of the differential equationu′=Au+fis identical with the spectrum offexcept at the origin, wherefis a weakly almost periodic function.

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 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.

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 On the stepanov almost periodic solution of a second-order infinitesimal generator differential equation

1991 ◽  
Vol 14 (4) ◽  
pp. 757-761 ◽  
Author(s):  
Aribindi Satyanarayan Rao
Keyword(s):  
Differential Equation ◽  
Banach Space ◽  
Periodic Solution ◽  
Infinitesimal Generator ◽  
Order Differential Equation ◽  
Reflexive Banach Space ◽  
Almost Periodic Solution ◽  
Second Order ◽  
Almost Periodic ◽  
Second Order Differential Equation

The Stepanov almost periodic solution of a certain second-order differential equation in a reflexive Banach space is shown to be almost periodic.

scholarly journals On first-order differential operators with Bohr-Neugebauer type property

1989 ◽  
Vol 12 (3) ◽  
pp. 473-476 ◽  
Author(s):  
Aribindi Satyanarayan Rao
Keyword(s):  
Differential Equation ◽  
Banach Space ◽  
Linear Operator ◽  
Real Line ◽  
Differential Operators ◽  
Bounded Solution ◽  
Almost Periodic ◽  
Bounded Linear ◽  
First Order ◽  
Type Property

We consider a differential equationddtu(t)-Bu(t)=f(t), where the functions u and f map the real line into a Banach space X and B: X→X is a bounded linear operator. Assuming that any Stepanov-bounded solution u is Stepanov almost-periodic when f is Bochner almost-periodic, we establish that any Stepanov-bounded solution u is Bochner almost-periodic when f is Stepanov almost-periodic. Some examples are given in which the operatorddt-B is shown to satisfy our assumption.

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