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Ufa Mathematical Journal, 2013, Volume 5, Issue 2, Pages 18–30
DOI: https://doi.org/10.13108/2013-5-2-18
(Mi ufa195)
 

This article is cited in 4 scientific papers (total in 4 papers)

On existence of nodal solution to elliptic equations with convex-concave nonlinearities

V. E. Bobkov

Institute of Mathematics CS USC RAS, Chernyshevskii str., 112, 450008, Ufa, Russia
References:
Abstract: In a bounded connected domain $\Omega \subset \mathbb{R}^N$, $N \geqslant 1$, with a smooth boundary, we consider the Dirichlet boundary value problem for elliptic equation with a convex-concave nonlinearity
\begin{equation*} \begin{cases} -\Delta u = \lambda |u|^{q-2} u + |u|^{\gamma-2} u, \quad x \in \Omega \\ u|_{\partial \Omega} = 0, \end{cases} \end{equation*}
where $1< q< 2< \gamma < 2^*$. As a main result, we prove the existence of a nodal solution to this equation on the nonlocal interval $\lambda \in (-\infty, \lambda_0^*)$, where $\lambda_0^*$ is determined by the variational principle of nonlinear spectral analysis via fibering method.
Keywords: nodal solution, convex-concave nonlinearity, fibering method.
Received: 05.03.2012
Russian version:
Ufimskii Matematicheskii Zhurnal, 2013, Volume 5, Issue 2, Pages 18–30
Bibliographic databases:
Document Type: Article
UDC: 517.9
Language: English
Original paper language: Russian
Citation: V. E. Bobkov, “On existence of nodal solution to elliptic equations with convex-concave nonlinearities”, Ufimsk. Mat. Zh., 5:2 (2013), 18–30; Ufa Math. J., 5:2 (2013), 18–30
Citation in format AMSBIB
\Bibitem{Bob13}
\by V.~E.~Bobkov
\paper On existence of nodal solution to elliptic equations with convex-concave nonlinearities
\jour Ufimsk. Mat. Zh.
\yr 2013
\vol 5
\issue 2
\pages 18--30
\mathnet{http://mi.mathnet.ru/ufa195}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3430773}
\elib{https://elibrary.ru/item.asp?id=19063033}
\transl
\jour Ufa Math. J.
\yr 2013
\vol 5
\issue 2
\pages 18--30
\crossref{https://doi.org/10.13108/2013-5-2-18}
Linking options:
  • https://www.mathnet.ru/eng/ufa195
  • https://doi.org/10.13108/2013-5-2-18
  • https://www.mathnet.ru/eng/ufa/v5/i2/p18
  • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Уфимский математический журнал
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    Abstract page:378
    Russian version PDF:121
    English version PDF:12
    References:78
    First page:2
     
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