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Mat. Zametki, 1992, Volume 52, Issue 1, Pages 51–56 (Mi mz4654)  

Multiple solvability of certain elliptic problems with critical nonlinearity exponents

I. A. Kuzin

Branch for Theoretical Problems, Russian Academy of Sciences

Abstract: It is proved that the problem
$$ \sum_{i=1}^N\nabla_i(|\nabla u|^{p-2}\nabla_iu)+|u|^{p^*-2}u+\lambda|u|^{q-2}u=0 in \Omega, \quad u=0 on \partial\Omega, $$
where $\Omega\subset\mathbf{R}^N$ a singly-connected region with an “odd” boundary, $N>p$, and $p^*=Np/(N-p)$ is a critical Sobolev exponent, has, under the appropriate conditions on $\lambda$, $q$ and $N$, no less than $(2N+2)$ nontrivial solutions in $\mathring{W}_{p^1}(\Omega)$.

Full text: PDF file (466 kB)

English version:
Mathematical Notes, 1992, 52:1, 668–672

Bibliographic databases:

UDC: 517
Received: 13.11.1991

Citation: I. A. Kuzin, “Multiple solvability of certain elliptic problems with critical nonlinearity exponents”, Mat. Zametki, 52:1 (1992), 51–56; Math. Notes, 52:1 (1992), 668–672

Citation in format AMSBIB
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\by I.~A.~Kuzin
\paper Multiple solvability of certain elliptic problems with critical nonlinearity exponents
\jour Mat. Zametki
\yr 1992
\vol 52
\issue 1
\pages 51--56
\mathnet{http://mi.mathnet.ru/mz4654}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1187713}
\zmath{https://zbmath.org/?q=an:0830.35040}
\transl
\jour Math. Notes
\yr 1992
\vol 52
\issue 1
\pages 668--672
\crossref{https://doi.org/10.1007/BF01247647}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1992LC62500008}


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