Journal of Mathematical Sciences

, Volume 236, Issue 4, pp 446–460 | Cite as

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

  • N. S. Ustinov

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 RR0 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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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.St.Petersburg State UniversitySt.PetersburgRussia

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