Existence And Nonexistence Of Solutions To Fractional Elliptic Equations With Hardy Potential

In this thesis,using the subsolution and supersolution method and the Schauder's fixed point theorem,we study the existence and nonexistence of solutions for two classes of fractional elliptic equations with Hardy potential.Firstly,we consider the existence and nonexistence of solutions to the following frac-tional elliptic equations with Hardy potential#12 where ?(?)RN is a bounded Lipschitz domain with 0??,(-?)s is a fractional Laplace operator,s ?(0,1),N>2s,? is a positive number,2<r<r(?,s)?N+2s-2??/N-2s-2??+1,???(0,N-2s/2)is a parameter depending on ?,0<?<?N,s,?N,s=22s?2(N+2s/4)/?2(N-2s/4)is the sharp constant of the Hardy-Sobolev inequality.Secondly,we study the existence and nonexistence of solutions to the following frac-tional elliptic equations with Hardy potential and singular non-linearity#12where?>0,?>0,1<p<p*,0<?<?N,s,?(?)RN is a bounded Lipschitz domain with0??.