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Singular boundary-value problems for ordinary second-order differential equations

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This article gives an exposition of the fundamental results of the theory of boundary-value problems for ordinary second-order differential equations having singularities with respect to the independent variable or one of the phase variables. In particular criteria are given for solvability and unique solvability of two-point boundary-value problems and problems concerning bounded and monotonic solutions. Several specific problems are considered which arise in applications (atomic physics, field theory, boundary-layer theory of a viscous incompressible fluid, etc.)

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  1. I. T. Kiguradze
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  2. B. L. Shekhter
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Translated from Itogi Nauki i Tekhniki, Seriya Sovremennye Problemy Matematiki, Noveishie Dostizheniya, Vol. 30, pp. 105–201, 1987.

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Kiguradze, I.T., Shekhter, B.L. Singular boundary-value problems for ordinary second-order differential equations. J Math Sci 43, 2340–2417 (1988). https://doi.org/10.1007/BF01100361

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