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The Neumann Problem for the Generalized Hénon Equation

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We study the behavior of radial solutions to the boundary value problem

$$ -{\varDelta}_pu+{u}^{p-1}={\left|x\right|}^a{u}^{q-1}\; in\;B,\kern1em \frac{\partial u}{\mathrm{\partial n}}=0\; on\;\partial B,\kern1em q>p, $$

in the unit ball B and prove the existence of nonradial positive solutions for some values of parameters. We obtain multiplicity results which are new even in the case p = 2.

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Authors and Affiliations

  1. Saint Petersburg Electrotechnical University “LETI”, 5, Professora Popova St, Saint Petersburg, 197276, Russia

    A. P. Shcheglova

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  1. A. P. Shcheglova
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Correspondence to A. P. Shcheglova.

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Translated from Problemy Matematicheskogo Analiza 95, 2018, pp. 103-114.

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Shcheglova, A.P. The Neumann Problem for the Generalized Hénon Equation. J Math Sci 235, 360–373 (2018). https://doi.org/10.1007/s10958-018-4078-4

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  • DOI: https://doi.org/10.1007/s10958-018-4078-4

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