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Multiple positive solutions of the Emden–Fowler equation in hollow thin symmetric domains

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Abstract

In this paper, we study the Emden–Fowler equation in a hollow thin symmetric domain \(\Omega \). Let \(H\) and \(G\) be closed subgroups of the orthogonal group such that \(H \varsubsetneq G\) and \(\Omega \) is \(G\) invariant. Then we prove the existence of an \(H\) invariant \(G\) non-invariant positive solution if the domain is thin enough and the orbits of \(H\) and \(G\) are different. Applying this theorem, we prove the existence of multiple positive solutions.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science and Engineering, Saga University, Saga, 840-8502, Japan

    Ryuji Kajikiya

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  1. Ryuji Kajikiya
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Correspondence to Ryuji Kajikiya.

Additional information

Communicated by P. Rabinowitz.

The author was supported in part by the Grant-in-Aid for Scientific Research (C) (No. 24540179), Japan Society for the Promotion of Science.

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Kajikiya, R. Multiple positive solutions of the Emden–Fowler equation in hollow thin symmetric domains. Calc. Var. 52, 681–704 (2015). https://doi.org/10.1007/s00526-014-0729-6

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  • DOI: https://doi.org/10.1007/s00526-014-0729-6

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