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Izv. RAN. Ser. Mat., 1995, Volume 59, Issue 1, Pages 103–120 (Mi izv4)  

On periodic non-trivial solutions of the equation $-\Delta u=g(u)$ in $\mathbb R^{N+1}$

Ya. Sh. Il'yasov


Abstract: The existence of non-trivial solutions of the equation $-\Delta u=g(u)$ in $\mathbb R^{N+1}$, which are periodic with large periods in one variable and rapidly decreasing in others, is proved using variational methods. The non-existence of such solutions for small periods is shown as well.

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English version:
Izvestiya: Mathematics, 1995, 59:1, 101–119

Bibliographic databases:

MSC: 35J25
Received: 22.02.1993

Citation: Ya. Sh. Il'yasov, “On periodic non-trivial solutions of the equation $-\Delta u=g(u)$ in $\mathbb R^{N+1}$”, Izv. RAN. Ser. Mat., 59:1 (1995), 103–120; Izv. Math., 59:1 (1995), 101–119

Citation in format AMSBIB
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\by Ya.~Sh.~Il'yasov
\paper On periodic non-trivial solutions of the equation $-\Delta u=g(u)$ in~$\mathbb R^{N+1}$
\jour Izv. RAN. Ser. Mat.
\yr 1995
\vol 59
\issue 1
\pages 103--120
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1328556}
\zmath{https://zbmath.org/?q=an:0837.35011}
\transl
\jour Izv. Math.
\yr 1995
\vol 59
\issue 1
\pages 101--119
\crossref{https://doi.org/10.1070/IM1995v059n01ABEH000004}
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  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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