Method of sub-super solutions for fractional elliptic equations

Authors

Yanqin Fang, University of WollongongFollow
De Tang, Sun Yat-Sen University

RIS ID

129847

Publication Details

Fang, Y. & Tang, D. (2018). Method of sub-super solutions for fractional elliptic equations. Discrete and Continuous Dynamical Systems - Series B, 23 (8), 3153-3165.

Abstract

By applying the method of sub-super solutions, we obtain the existence of weak solutions to fractional Laplacian (Formula Presented) where f :Ω x R → R is a Caratheodory function. Let v be a Radon measure. Based on the existence result in (1), we derive the existence of weak solutions for the semilinear fractional elliptic equation with measure data (Formula Presented) Some results in [7] are extended. In addition, we generalize some results to systems of fractional Laplacian equations by constructing subsolutions and supersolutions.