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Zbl 1065.34053
Agarwal, Ravi P.; O'Regan, Donal; Zernov, Oleksandr E.
A singular initial value problem for some functional differential equations.
(English)
[J] J. Appl. Math. Stochastic Anal. 2004, No. 3, 261-270 (2004). ISSN 1048-9533; ISSN 1687-2177/e

Summary: For the initial value problem $t^rx'(t)=at+b_1x(t)+ b_2 x(q_1t)+b_3t^rx' (q_2t)+\varphi(t,x(t)$, $x(q_1t),x'(t),x'(q_2t))$, $x(0) =0$, where $r>1$, $0<q_i \le 1$, $i\in\{1,2\}$, we find a nonempty set of continuously differentiable solutions $x:(0,\rho]\to \bbfR$, each of which possesses nice asymptotic properties when $t\to+0$.
MSC 2000:
*34K05 General theory of functional-differential equations

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