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Almost periodic solutions of differential equations with piecewise constant argument of generalized type
Authors:MU Akhmet  
Institution:

aDepartment of Mathematics and Institute of Applied Mathematics, Middle East Technical University, 06531 Ankara, Turkey

Abstract:We consider the existence and stability of an almost periodic solution of the following hybrid system:
(1)
View the MathML source
where View the MathML source if θit<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. A new technique of investigation of equations with piecewise argument, based on integral representation, is developed.
Keywords:Quasilinear system  Almost periodic solutions  Piecewise constant argument of general type  Advanced–delayed argument
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