Existence of a minimal positive solutions for some singularity elliptic equation

Caratheodory function, that is for x x∈Ω, (g , )u can be measured, for u R x, (g , )u is continuous, and simultaneously satisfies the growth conditions

g u u ep( ,x ) (C ) .a . ,+ −1 1 Ω

where 2 2p *. If u H0 1( ) is a weak solution

of −Δu u− xμ / (x g= , )u2 , then for any r > 0 satisfied Br ( ) ⊂ Ω such that u L Br

∞( \ ( )), further u C Bloc r

1, ( \ ( )0 )α .