半线性蜕缩椭圆型方程的Dirichlet问题

设Ω(?)R~n(n≥2)是光滑有界区域.讨论如下的半线性蜕缩椭圆型方程的Dirichlet问题Lu ≡-sum from i,j=1 to n((?)/(?)x_i)(aij(x)((?)u/(?)xj)=g(x,u) (x,u),在Ω中,u=0,在(?)Ω上。(1)这里,且sum from i,j=1 to n(aijξiξj≥k sum from i=1 to n(ρ~a_i(x)ξ_i~2),(?)x∈(?),(?)ξ∈R~n,(2)