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The Neumann boundary value problem for a semilinear elliptic equation in a thin cylinder. The least energy solutions

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Abstract

It is proved that the least energy solution of the BVP

$$ \left\{ \begin{gathered} - \Delta u + u = |u|^{q - 2} uinQ, \hfill \\ \tfrac{{\partial u}} {{\partial n}} = 0on\partial Q, \hfill \\ \end{gathered} \right. $$

, is a constant for all q ∈ (2; 2*] if Q ⊂ ℝn (n ≥ 3) is a sufficiently thin cylinder. Bibliography: 8 titles.

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Authors and Affiliations

  1. St.Petersburg State Electrotechnical University, St.Petersburg, Russia

    A. P. Shcheglova

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  1. A. P. Shcheglova
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__________

Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 348, 2007, pp. 272–302.

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Shcheglova, A.P. The Neumann boundary value problem for a semilinear elliptic equation in a thin cylinder. The least energy solutions. J Math Sci 152, 780–798 (2008). https://doi.org/10.1007/s10958-008-9089-0

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  • DOI: https://doi.org/10.1007/s10958-008-9089-0

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