Publication details
Boundary singularities of solutions to semilinear fractional equations
| Authors | |
|---|---|
| Year of publication | 2018 |
| Type | Peer-reviewed scientific article |
| Magazine / Source | Advanced Nonlinear Studies |
| MU Faculty or unit | |
| Citation | |
| web | https://www.degruyter.com/view/j/ans.2018.18.issue-2/ans-2017-6048/ans-2017-6048.xml |
| Doi | https://doi.org/10.1515/ans-2017-6048 |
| 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). |