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Contemporary Mathematics. Fundamental Directions
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Contemporary Mathematics. Fundamental Directions, 2006, Volume 16, Pages 10–21 (Mi cmfd45)  
This article is cited in 2 scientific papers (total in 2 papers)

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

M. K. Grammatikopulosa, P. S. Kelevedzhievb, N. I. Popivanovc

a University of Ioannina
b Technical University of Sofia
c Sofia University St. Kliment Ohridski
Full-text PDF (203 kB) Citations (2)
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Abstract: 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 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.
English version:
Journal of Mathematical Sciences, 2008, Volume 149, Issue 5, Pages 1504–1516
DOI: https://doi.org/10.1007/s10958-008-0079-z
Bibliographic databases:
UDC: 517.911+517.927.21
Language: Russian
Citation: M. K. Grammatikopulos, P. S. Kelevedzhiev, N. I. Popivanov, “On the solvability of a singular boundary-value problem for the equation f(t,x,x′,x″)=0”, Proceedings of the Fourth International Conference on Differential and Functional-Differential Equations (Moscow, August 14–21, 2005). Part 2, CMFD, 16, PFUR, M., 2006, 10–21; Journal of Mathematical Sciences, 149:5 (2008), 1504–1516
Citation in format AMSBIB
\Bibitem{GraKelPop06}
\by M.~K.~Grammatikopulos, P.~S.~Kelevedzhiev, N.~I.~Popivanov
\paper On the solvability of a~singular boundary-value problem for the equation $f(t,x,x',x'')=0$
\inbook Proceedings of the Fourth International Conference on Differential and Functional-Differential Equations (Moscow, August 14--21, 2005). Part~2
\serial CMFD
\yr 2006
\vol 16
\pages 10--21
\publ PFUR
\publaddr M.
\mathnet{http://mi.mathnet.ru/cmfd45}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2336442}
\transl
\jour Journal of Mathematical Sciences
\yr 2008
\vol 149
\issue 5
\pages 1504--1516
\crossref{https://doi.org/10.1007/s10958-008-0079-z}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84907538431}
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  • https://www.mathnet.ru/eng/cmfd45
  • https://www.mathnet.ru/eng/cmfd/v16/p10
    • This publication is cited in the following 2 articles:
    1. Petio Kelevedjiev, Nedyu Popivanov, “Second-order initial value problems with singularities”, Bound Value Probl, 2014:1 (2014)  crossref
    2. P Palamides, P Kelevedjiev, N Popivanov, “On the solvability of a Neumann boundary value problem for the differential equation “Equation missing””, Bound Value Probl, 2012:1 (2012)  crossref
    Citing articles in Google Scholar: Russian citations, English citations
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