Almost periodic solutions of differential equations with piecewise constant argument of generalized type

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2008-06-01

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Akhmet, Marat

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We consider existence and stability of an almost periodic solution of the following hybrid system dx(t) dt = A(t)x(t) + f(t, x(θβ(t)−p1 ), x(θβ(t)−p2 ), . . . , x(θβ(t)−pm )), (1) where x ∈ R n , t ∈ R, β(t) = i if θi ≤ t < θi+1, i = . . .−2, −1, 0, 1, 2, . . . , is an identification function, θi is a strictly ordered sequence of real numbers, unbounded on the left and on the right, pj , 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. The problem of positive (almost periodic) solutions of the logistic equation is discussed as an example. A new technique of investigation of equations with piecewise argument, based on integral representation, is developed.

Subject Keywords

Control and Systems Engineering, Analysis, Computer Science Applications

URI

https://hdl.handle.net/11511/47331

Journal

NONLINEAR ANALYSIS-HYBRID SYSTEMS

DOI

https://doi.org/10.1016/j.nahs.2006.09.002

Collections

Department of Mathematics, Article

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Citation Formats

M. Akhmet, “Almost periodic solutions of differential equations with piecewise constant argument of generalized type,” NONLINEAR ANALYSIS-HYBRID SYSTEMS, pp. 456–467, 2008, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/47331.