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Anti-periodic solutions of nonlinear first order impulsive functional differential equations. (English) Zbl 1274.34229

Summary: The existence of anti-periodic solutions of the following nonlinear impulsive functional differential equation \[ x'(t)+a(t)x(t)=f\Bigl (t,x(t),x\bigl (\alpha _1(t)\bigr), \ldots ,x\bigl (\alpha _n(t)\bigr)\Bigr), \qquad t\in \mathbb R, \]
\[ \Delta x(t_k)=I_k\bigl (x(t_k)\bigr), \qquad k\in \mathbb Z \] is studied. Sufficient conditions for the existence of at least one anti-periodic solution are established. Several new existence results are obtained.

MSC:

34K45 Functional-differential equations with impulses
34K13 Periodic solutions to functional-differential equations
47N20 Applications of operator theory to differential and integral equations
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