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Zbl 1218.34096
Shao, Yuanfu; Zhou, Yonghui
Existence of an exponential periodic attractor of a class of impulsive differential equations with time-varying delays.
(English)
[J] Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 74, No. 4, 1107-1118 (2011). ISSN 0362-546X

For the system $$\dot{x}_i(t)=-a_i(t)x_i(t)+f_i(x_1(t),\dots,x_n(t),x_1(t-\tau_{i1}),\dots, x_n(t-\tau_{in})), \quad t\neq t_k,$$ $$\Delta x_i(t_k)=x_i(t_k^+)-x_i(t_k^-)=J_k(x_i(t_k))$$ existence and exponential stability of a periodic solution are established. The obtained results are compared with some known ones.
[Leonid Berezanski (Beer-Sheva)]
MSC 2000:
*34K45 Equations with impulses
34K20 Stability theory of functional-differential equations
34K13 Periodic solutions of functional differential equations
47N20 Appl. of operator theory to differential and integral equations

Keywords: impulsive delay differential equation; periodic attractor; continuation theorem

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