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Asymptotic behavior of the solutions of a partial differential equation with piecewise constant argument
  • Garyfalos Papaschinopoulos,
  • G. Stefanidou
Garyfalos Papaschinopoulos
Democritus University of Thrace

Corresponding Author:[email protected]

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G. Stefanidou
Democritus University of Thrace
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Abstract

In this paper we study the partial differential equation with piecewise constant argument of the form : \[ \begin{array}{lll} x_t(t,s)=&A(t)x(t,s)+B(t,s)x([t],s)+C(t,s)x(t,[s])+\\[0.5cm] &D(t,s)x([t],[s])+f(x(t,[s])),\ \ t,s\in \R^{+}=(0,\infty) \end{array} \] where $A(t)$ is a $k\times k$ invertible and continuous matrix function on $\R^{+}$, $B(t,s)$, $C(t,s)$, $D(t,s)$ are $k \times k$ continuous and bounded matrix functions on $\R^{+}\times \R^{+}$, $[t]$, $[s]$ are the integral parts of $t,s$ respectively and $f:\R^k\rightarrow \R^k$ is a continuous function. More precisely under some conditions on the matrices $A(t)$, $B(t,s)$, $C(t,s)$, $D(t,s)$ and the function $f$ we investigate the asymptotic behaviour of the solutions of the above equation. \end{abstract}
18 May 2022Submitted to Mathematical Methods in the Applied Sciences
19 May 2022Submission Checks Completed
19 May 2022Assigned to Editor
28 May 2022Reviewer(s) Assigned
21 Jun 2022Review(s) Completed, Editorial Evaluation Pending
22 Jun 2022Editorial Decision: Revise Major
24 Jun 20221st Revision Received
25 Jun 2022Submission Checks Completed
25 Jun 2022Assigned to Editor
25 Jun 2022Reviewer(s) Assigned
25 Jun 2022Review(s) Completed, Editorial Evaluation Pending
26 Jun 2022Editorial Decision: Revise Minor
26 Jun 20222nd Revision Received
27 Jun 2022Submission Checks Completed
27 Jun 2022Assigned to Editor
27 Jun 2022Review(s) Completed, Editorial Evaluation Pending
27 Jun 2022Editorial Decision: Accept