, Volume 149, Issue 5, pp 1504-1516

On the solvability of a singular boundary-value problem for the equation f(t, x, x′, x″) = 0

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In this work, we consider boundary-value problems of the form $$f(t, x, x', x'') = 0, 0 < t < 1, x(0) = 0, x'(1) = b, b > 0$$ , where the scalar function f(t, x, p, q) may be singular at x = 0. As far as we know, the solvability of the singular boundary-value problems of this form has not been treated yet. Here we try to fill in this gap. Examples illustrating our main result are included.

Translated from Sovremennaya Matematika. Fundamental’nye Napravleniya (Contemporary Mathematics. Fundamental Directions), Vol. 16, Differential and Functional Differential Equations. Part 2, 2006.