A singular initial value problem for some functional differential equations

Ravi P. Agarwal; Donal O'Regan; Oleksandr Zernov

doi:10.1155/S1048953304405012

A singular initial value problem for some functional differential equations

Ravi P. Agarwal
, Donal O'Regan
, Oleksandr Zernov

Mathematics

Research output: Contribution to a Journal (Peer & Non Peer) › Article › peer-review

5 Citations (Scopus)

Abstract

For the initial value problem t^r x′ (t) = at + b₁x(t) + b₂x (q₁t) + b₃ t^r x′ (q₂t) + φ(t, x(t), x(q₁t), x′ (t), x′ (q₂t)), x(0) = 0, where r > 1, 0 < q_i ≤ 1, i ∈ {1,2}, we find a nonempty set of continuously differentiable solutions x: (0, ρ] → ℝ, each of which possesses nice asymptotic properties when t → + 0.

Original language	English
Pages (from-to)	261-270
Number of pages	10
Journal	Journal of Applied Mathematics and Stochastic Analysis
Volume	2004
Issue number	3
DOIs	https://doi.org/10.1155/S1048953304405012
Publication status	Published - 2004

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AU - O'Regan, Donal

AU - Zernov, Oleksandr

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AB - For the initial value problem tr x′ (t) = at + b1x(t) + b2x (q1t) + b3 tr x′ (q2t) + φ(t, x(t), x(q1t), x′ (t), x′ (q2t)), x(0) = 0, where r > 1, 0 < qi ≤ 1, i ∈ {1,2}, we find a nonempty set of continuously differentiable solutions x: (0, ρ] → ℝ, each of which possesses nice asymptotic properties when t → + 0.

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ER -

A singular initial value problem for some functional differential equations

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