Almost periodic solutions of differential equations with piecewise constant argument of generalized type
By Marat U. Akhmet. 2006
157 citations recorded by the source corpus.
Abstract We consider the existence and stability of an almost periodic solution of the following hybrid system: (1) d x ( t ) d t = A ( t ) x ( t ) + f ( t , x ( θ β ( t ) − p 1 ) , x ( θ β ( t ) − p 2 ) , … , x ( θ β ( t ) − p m ) ) , where x ∈ R n , t ∈ R , β ( t ) = i if θ i ≤ t θ i + 1 , i = … − 2 , − 1 , 0 , 1 , 2 , … , is an identification function, θ i is a strictly ordered sequence of real numbers, unbounded on the left and on the right, p j , j = 1 , 2 , … , m , are fixed integers, and the linear homogeneous system associated with (1) satisfies exponential dichotomy. The deviations of the argument are not restricted by any sign assumption when existence is considered. A new technique of investigation of equations with piecewise argument, based on integral representation, is developed.
Subfields: Applied Mathematics, Numerical Analysis
View Paper: https://www.semanticscholar.org/paper/ccde085e55582592a8fc8b8d54915ad89c5ec4f8
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In Applied Mathematics
In Numerical Analysis
Citations in the corpus
- Periodic solutions of differential equations with a general piecewise constant argument and applications (2010, background): “Remark 3 Recently, in [3]-[4], Akhmet obtained fundamental results about the variation of constants formula, existence and uniqueness of solutions of the perturbed system (1.”
- Cauchy and Green matrices type and stability in alternately advanced and delayed differential systems (2011, methodology): “DEPCAG, when zi 1⁄4 ti; i [ Z, an only delayed situation was considered for the first time by Akhmet [3].”