Electron. J. Diff. Equ., Vol. 2014 (2014), No. 210, pp. 1-9.

Asymptotic behavior of solutions to mixed type differential equations

Sandra Pinelas

Abstract:
This work concerns the asymptotic behavior of solutions to the differential equation
$$ \dot{x}(t)+\sum_{i=1}^{m}a_i(t)x(r_i(t))+\sum_{j=1}^{n}b_j(t)x(\tau_j(t))=0, $$
where $a_j(t)$ and $b_j(t)$ are real-valued continuous functions and $r_j(t)$ and $\tau_j(t)$ are non-negative functions such that
$$\displaylines{ r_i(t)\leq t,\; t\geq t_0,\quad\lim_{t\to \infty}r_i(t)=\infty,\; i=1,\dots,m;\cr \tau_j(t)\geq t,\; t\geq t_0,\quad\lim_{t\to \infty}\tau_j(t)=\infty,\; j=1, \dots,n. }$$

Submitted May 5, 2014. Published October 10, 2014.
Math Subject Classifications: 34K06, 34D04, 47H10.
Key Words: Differential equations; fixed point; asymptotic behavior.

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Sandra Pinelas
Academia Militar
Departamento de Ciências Exatas e Naturais
Conde Castro Guimarães, Amadora, Portugal
email: sandra.pinelas@gmail.com

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