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Multiplicity of Positive Solutions to the Boundary-Value Problems for Fractional Laplacians

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For the problem (−Δ)su=uq−1 in the annulus ΩR = BR+1 \ BR ∈ ℝn, a so-called “multiplicity effect” is established: for each N ∈ ℕ there exists R0 such that for all R ≥ R0 this problem has at least N different positive solutions. (−Δ)s in this problem stands either for Navier-type or for Dirichlet-type fractional Laplacian. Similar results were proved earlier for the equations with the usual Laplace operator and with the p-Laplacian operator.

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Authors and Affiliations

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

    N. S. Ustinov

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  1. N. S. Ustinov
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Correspondence to N. S. Ustinov.

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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 459, 2017, pp. 104–126.

Translated by I. Ponomarenko.

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Ustinov, N.S. Multiplicity of Positive Solutions to the Boundary-Value Problems for Fractional Laplacians. J Math Sci 236, 446–460 (2019). https://doi.org/10.1007/s10958-018-4124-2

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  • DOI: https://doi.org/10.1007/s10958-018-4124-2

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