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Zapiski Nauchnykh Seminarov POMI, 2016, Volume 444, Pages 98–109 (Mi znsl6270)  
This article is cited in 3 scientific papers (total in 3 papers)

The multiplicity of positive solutions to the quasilinear equation generated by the Il'in–Caffarelli–Kohn–Nirenberg inequality

A. I. Nazarovab, B. O. Neterebskiic

a St. Petersburg State University, St. Petersburg, Russia
b St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences, St. Petersburg, Russia
c St. Petersburg, Russia
Full-text PDF (215 kB) Citations (3)
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Abstract: We consider the Euler–Lagrange equation for the functional related to the V. P. Il'in inequality also known as the Caffarelli–Kohn–Nirenberg inequality. We prove that if the space dimension is even then, changing some parameters, we can obtain arbitrary many different positive solutions for this equation.
Key words and phrases: quasilinear equations, the Caffarelli–Kohn–Nirenberg inequality, multiplicity of solutions.
Funding agency Grant number
Saint Petersburg State University 6.38.670.2013
Russian Foundation for Basic Research 14-01-00534
Received: 12.11.2015
English version:
Journal of Mathematical Sciences (New York), 2017, Volume 224, Issue 3, Pages 448–455
DOI: https://doi.org/10.1007/s10958-017-3427-z
Bibliographic databases:
Document Type: Article
UDC: 517
Language: Russian
Citation: A. I. Nazarov, B. O. Neterebskii, “The multiplicity of positive solutions to the quasilinear equation generated by the Il'in–Caffarelli–Kohn–Nirenberg inequality”, Boundary-value problems of mathematical physics and related problems of function theory. Part 45, Zap. Nauchn. Sem. POMI, 444, POMI, St. Petersburg, 2016, 98–109; J. Math. Sci. (N. Y.), 224:3 (2017), 448–455
Citation in format AMSBIB
\Bibitem{NazNet16}
\by A.~I.~Nazarov, B.~O.~Neterebskii
\paper The multiplicity of positive solutions to the quasilinear equation generated by the Il'in--Caffarelli--Kohn--Nirenberg inequality
\inbook Boundary-value problems of mathematical physics and related problems of function theory. Part~45
\serial Zap. Nauchn. Sem. POMI
\yr 2016
\vol 444
\pages 98--109
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6270}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3509679}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2017
\vol 224
\issue 3
\pages 448--455
\crossref{https://doi.org/10.1007/s10958-017-3427-z}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85020176406}
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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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