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Zapiski Nauchnykh Seminarov POMI, 2006, Volume 336, Pages 25–45 (Mi znsl195)  
This article is cited in 16 scientific papers (total in 16 papers)

On solvability of Dirichlet problem to semilinear Schrödinger equation with singular potential

A. V. Demyanov, A. I. Nazarov

Saint-Petersburg State University
Full-text PDF (264 kB) Citations (16)
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Abstract: We prove the existence of a positive solution to the Dirichlet problem for the semilinear Schrödinger equation with acritical singular potential. We assume that the boundary $\partial\Omega$ is average concave at the origin.
Received: 14.08.2006
English version:
Journal of Mathematical Sciences (New York), 2007, Volume 143, Issue 2, Pages 2857–2868
DOI: https://doi.org/10.1007/s10958-007-0171-9
Bibliographic databases:
UDC: 517
Language: Russian
Citation: A. V. Demyanov, A. I. Nazarov, “On solvability of Dirichlet problem to semilinear Schrödinger equation with singular potential”, Boundary-value problems of mathematical physics and related problems of function theory. Part 37, Zap. Nauchn. Sem. POMI, 336, POMI, St. Petersburg, 2006, 25–45; J. Math. Sci. (N. Y.), 143:2 (2007), 2857–2868
Citation in format AMSBIB
\Bibitem{DemNaz06}
\by A.~V.~Demyanov, A.~I.~Nazarov
\paper On solvability of Dirichlet problem to semilinear Schr\"odinger equation with singular potential
\inbook Boundary-value problems of mathematical physics and related problems of function theory. Part~37
\serial Zap. Nauchn. Sem. POMI
\yr 2006
\vol 336
\pages 25--45
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl195}
\mathscinet{https://mathscinet.ams.org/mathscinet-getitem?mr=2270878}
\zmath{https://zbmath.org/?q=an:1136.35088}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2007
\vol 143
\issue 2
\pages 2857--2868
\crossref{https://doi.org/10.1007/s10958-007-0171-9}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-34247350282}
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    • This publication is cited in the following 16 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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