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Oscillatory regimes of solutions of linear differential equations with generalized perturbations.
 

Summary: Oscillatory regimes of solutions of linear differential
equations with generalized perturbations.
Isaac Dontwi
Kwame Nkrumah University of Science and Technology, Ghana
The notion of boundedness, almost-periodicity, asymptotically almost-
periodicity, exponential dichotomy, regularity, permissibility, etc. play
very important role in the Qualitative Theory of Linear Differential
Equations. The current exposition is in this direction and is devoted
to the problem of boundedness, almost-periodicity and asymptotically
almost-periodicity of the solutions of linear differential equations with
generalized perturbations (Distributions). In the last several years the
theory of linear differential equations has seen a boost in research re-
sults in this direction by a host of mathematicians. Some classical
work in the theory of impulse system include monographs by A.M.
Samoilenko, N.A. Petrovskii, Halanai and D. Wexler etc. The beat
system in linear case is equivalent to impulse system of the form be-
low:
(1) dX/dt = A(t)X + k Skk
It is worth considering the general systems with generalized pertur-
bation of the form

  

Source: Assani, Idris - Department of Mathematics, University of North Carolina at Chapel Hill

 

Collections: Mathematics