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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2017, Volume 132, Pages 91–94 (Mi into173)  
On the solvability of a boundary-value problem for a second-order singular quasilinear equation

V. P. Plaksina, I. M. Plaksina, È. V. Plekhova

Perm State National Research Polytechnical University, Applied Mathematics and Mechanics Faculty
Full-text PDF (267 kB)
Abstract: We obtain solvability conditions for a two-point boundary-value problem for a second-order quasilinear equation. The equation is singular with respect to the independent variable. The result is based on the properties of the Green operator of the corresponding linear problem. In particular, we prove its boundedness and obtain an upper estimate of its norm. Conditions of the existence of a solution of the original problem are obtained from the solvability condition of an auxiliary operator equation.
Keywords: singular ordinary differential equation, boundary-value problem, Green operator, quasilinear equation.
Funding agency Grant number
Russian Foundation for Basic Research 14-01-00338_à
English version:
Journal of Mathematical Sciences (New York), 2018, Volume 230, Issue 5, Pages 742–745
DOI: https://doi.org/10.1007/s10958-018-3781-5
Bibliographic databases:
Document Type: Article
UDC: 527.927
MSC: 34B05, 34B16
Language: Russian
Citation: V. P. Plaksina, I. M. Plaksina, È. V. Plekhova, “On the solvability of a boundary-value problem for a second-order singular quasilinear equation”, Proceedings of International Symposium “Differential Equations–2016”, Perm, May 17-18, 2016, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 132, VINITI, Moscow, 2017, 91–94; J. Math. Sci. (N. Y.), 230:5 (2018), 742–745
Citation in format AMSBIB
\Bibitem{PlaPlaPle17}
\by V.~P.~Plaksina, I.~M.~Plaksina, \`E.~V.~Plekhova
\paper On the solvability of a boundary-value problem for a second-order singular quasilinear equation
\inbook Proceedings of International Symposium “Differential Equations–2016”, Perm, May 17-18, 2016
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2017
\vol 132
\pages 91--94
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into173}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3801393}
\zmath{https://zbmath.org/?q=an:1392.34018}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2018
\vol 230
\issue 5
\pages 742--745
\crossref{https://doi.org/10.1007/s10958-018-3781-5}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85044455049}
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