Behavior at infinity of solutions of an operator differential equation of first order in a Banach space

1989 ◽  
Vol 40 (5) ◽  
pp. 536-538
Author(s):  
V. M. Gorbachuk
Keyword(s):  
Differential Equation ◽  
Banach Space ◽  
Operator Differential Equation ◽  
First Order

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.

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 Differential Equation in a Banach Space Multiplicatively Perturbed by Random Noise

2017 ◽  
Vol 63 (4) ◽  
pp. 599-614
Author(s):  
V G Zadorozhniy ◽  
M A Konovalova
Keyword(s):  
Differential Equation ◽  
Banach Space ◽  
Random Noise ◽  
Random Coefficients ◽  
First Order ◽  
The Cauchy Problem ◽  
Moment Functions ◽  
Nonhomogeneous Differential Equation ◽  
Variational Derivatives ◽  
The Moment

We consider the problem of finding the moment functions of the solution of the Cauchy problem for a first-order linear nonhomogeneous differential equation with random coefficients in a Banach space. The problem is reduced to the initial problem for a nonrandom differential equation with ordinary and variational derivatives. We obtain explicit formula for the mathematical expectation and the second-order mixed moment functions for the solution of the equation.

scholarly journals Differential equations in Banach spaces

1973 ◽  
Vol 9 (2) ◽  
pp. 219-226 ◽  
Author(s):  
E.S. Noussair
Keyword(s):  
Differential Equation ◽  
Banach Space ◽  
Hilbert Space ◽  
Differential Equations ◽  
Banach Spaces ◽  
Linear Operators ◽  
Operator Differential Equation ◽  
Bounded Linear ◽  
Image Position ◽  
Scalar Differential Equation

Let H be a fixed Hilbert space and B(H, H) be the Banach space of bounded linear operators from H to H with the uniform operator topology. Oscillation criteria are obtained for the operator differential equationwhere the coefficients A, C are linear operators from B(H, H) to B(H, H), for each t ≤ 0. A solution Y: R+ → B(H, H) is said to be oscillatory if there exists a sequence of points ti ∈ R+, so that ti → ∞ as i → ∞, and Y(ti) fails to have a bounded inverse. The main theorem states that a solution Y is oscillatory if an associated scalar differential equation is oscillatory.

scholarly journals On the Hyers-Ulam stability of a first order partial differential equation

2012 ◽  
Vol 28 (1) ◽  
pp. 77-82
Author(s):  
NICOLAIE LUNGU ◽  
◽  
DORIAN POPA ◽  
Keyword(s):  
Differential Equation ◽  
Banach Space ◽  
Partial Differential Equation ◽  
Linear Partial Differential Equation ◽  
Order Partial Differential Equation ◽  
Ulam Stability ◽  
Partial Differential ◽  
First Order

We obtain a result on Hyers-Ulam stability for a linear partial differential equation of order one in a Banach space.

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