Informace o publikaci

Boundary singularities of solutions to semilinear fractional equations

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NGUYEN Phuoc-Tai VÉRON Laurent

Rok publikování 2018
Druh Článek v odborném periodiku
Časopis / Zdroj Advanced Nonlinear Studies
Fakulta / Pracoviště MU

Přírodovědecká fakulta

Citace
www https://www.degruyter.com/view/j/ans.2018.18.issue-2/ans-2017-6048/ans-2017-6048.xml
Doi http://dx.doi.org/10.1515/ans-2017-6048
Klíčová slova s-Harmonic Functions;Semilinear Fractional Equations;Boundary Trace
Popis We prove the existence of a solution of (-Delta)(s)u + f(u) = 0 in a smooth bounded domain Omega with a prescribed boundary value mu in the class of Radon measures for a large class of continuous functions f satisfying a weak singularity condition expressed under an integral form. We study the existence of a boundary trace for positive moderate solutions. In the particular case where f(u) = u(p) and mu is a Dirac mass, we show the existence of several critical exponents p. We also demonstrate the existence of several types of separable solutions of the equation (-Delta)(s)u + u(p) = 0 in R-+(N).