A singular initial value problem for some functional differential equations

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

International Journal of Stochastic Analysis, 2004, vol. 2004, 1-10

Abstract:

For the initial value problem t r x ′ ( t ) = a t + b 1 x ( t ) + b 2 x ( q 1 t ) + b 3 t r x ′ ( q 2 t ) + φ ( t , x ( t ) , x ( q 1 t ) , x ′ ( t ) , x ′ ( q 2 t ) ) , 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 .

Date: 2004
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnijsa:570368

DOI: 10.1155/S1048953304405012

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