Almost periodic solutions of differential equations with piecewise constant argument of generalized type |
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Authors: | MU Akhmet |
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Institution: | aDepartment of Mathematics and Institute of Applied Mathematics, Middle East Technical University, 06531 Ankara, Turkey |
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Abstract: | We consider the existence and stability of an almost periodic solution of the following hybrid system: where 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. A new technique of investigation of equations with piecewise argument, based on integral representation, is developed. |
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Keywords: | Quasilinear system Almost periodic solutions Piecewise constant argument of general type Advanced–delayed argument |
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