Existence of solutions for the Dirichlet problem of some degenerate semilinear elliptic equations

In this work we are interested in the existence of solutions for Dirichlet problems associated with the degenerate semilinear elliptic equations − ∑ i , j = 1 n D j ( a i j ( x ) D i u ( x ) ) − μ u ( x ) g ( x ) = − f ( x , u ( x ) ) on  Ω in the setting of the weighted Sobolev spaces W 0 1 , 2 ( Ω , ω ) .