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Izv. RAN. Ser. Mat., 1993, Volume 57, Issue 5, Pages 149–167 (Mi izv844)  

Comparison theorems for variational problems and their application to elliptic equations in $\mathbf R^N$

I. A. Kuzin


Abstract: The behavior of PS-sequences for problems of the form
$$ \begin{cases} -\sum\limits_{i=1}^N \nabla_ia_i(\mathbf x,u,\nabla u)+b(\mathbf x,u,\nabla u)=0 \quadin\quad \mathbf R^N,
u\to 0 \quadas\quad |\mathbf x|\to\infty \end{cases} $$
with functions $a_i,b\colon(\mathbf x, \mu,\xi)\mapsto c$ odd with respect to $\mu$, $\xi$ and such that $a_i(\mathbf x, \mu,\xi)\to\bar a_i(\mu,\xi)$, $b(\mathbf x, \mu,\xi)\to\bar b(\mu,\xi)$ as $|\mathbf x|\to\infty$, is studied. On the basis of this, theorems are proved on the existence of $l$ distinct pairs of nontrivial solutions of this problem.

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English version:
Russian Academy of Sciences. Izvestiya Mathematics, 1994, 43:2, 331–346

Bibliographic databases:

UDC: 517.95
MSC: 35B05, 35J20
Received: 15.08.1991

Citation: I. A. Kuzin, “Comparison theorems for variational problems and their application to elliptic equations in $\mathbf R^N$”, Izv. RAN. Ser. Mat., 57:5 (1993), 149–167; Russian Acad. Sci. Izv. Math., 43:2 (1994), 331–346

Citation in format AMSBIB
\Bibitem{Kuz93}
\by I.~A.~Kuzin
\paper Comparison theorems for variational problems and their application to elliptic
equations in $\mathbf R^N$
\jour Izv. RAN. Ser. Mat.
\yr 1993
\vol 57
\issue 5
\pages 149--167
\mathnet{http://mi.mathnet.ru/izv844}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1252760}
\zmath{https://zbmath.org/?q=an:0821.35009}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?1994IzMat..43..331K}
\transl
\jour Russian Acad. Sci. Izv. Math.
\yr 1994
\vol 43
\issue 2
\pages 331--346
\crossref{https://doi.org/10.1070/IM1994v043n02ABEH001567}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1994QC45400007}


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  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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