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On the solvability of a singular boundaryvalue problem for the equation f(t, x, x′, x″) = 0
 M. K. Grammatikopoulos,
 P. S. Kelevedjiev,
 N. I. Popivanov
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In this work, we consider boundaryvalue 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 boundaryvalue problems of this form has not been treated yet. Here we try to fill in this gap. Examples illustrating our main result are included.
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Translated from Sovremennaya Matematika. Fundamental’nye Napravleniya (Contemporary Mathematics. Fundamental Directions), Vol. 16, Differential and Functional Differential Equations. Part 2, 2006.
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 Title
 On the solvability of a singular boundaryvalue problem for the equation f(t, x, x′, x″) = 0
 Journal

Journal of Mathematical Sciences
Volume 149, Issue 5 , pp 15041516
 Cover Date
 20080301
 DOI
 10.1007/s109580080079z
 Print ISSN
 10723374
 Online ISSN
 15738795
 Publisher
 Springer US
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 Authors

 M. K. Grammatikopoulos ^{(1)}
 P. S. Kelevedjiev ^{(2)}
 N. I. Popivanov ^{(3)}
 Author Affiliations

 1. Department of Mathematics, University of Ioannina, Ioannina, Greece
 2. Department of Mathematics, Technical University of Sliven, Sliven, Bulgaria
 3. Department of Mathematics, “St. Kl. Ohridski” University of Sofia, Sofia, Bulgaria