Publication details

Boundary singularities of solutions to semilinear fractional equations


NGUYEN Phuoc-Tai VÉRON Laurent

Year of publication 2018
Type Article in Periodical
Magazine / Source Advanced Nonlinear Studies
MU Faculty or unit

Faculty of Science

Keywords s-Harmonic Functions;Semilinear Fractional Equations;Boundary Trace
Description 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).

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