Method of sub-super solutions for fractional elliptic equations
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  are extended. In addition, we generalize some results to systems of fractional Laplacian equations by constructing subsolutions and supersolutions.