On quasilinear elliptic equations related to some Caffarelli-Kohn-Nirenberg inequalities

The present work is devoted to analyze the Dirichlet problem for quasilinear elliptic equation related to some Caffarelli-Kohn-Nirenberg inequalities. Precisely the problem under study is, -div(\x\-pgamma\delu\p-2delu)=f(x,u)is an element ofL(1)(Omega), xis an element ofOmega u(x) = 0 on partial derivativeOmega, where -infinity < gamma < N - p/p, Omega is a bounded domain in R-N such that 0 is an element of Omega and f(x,u) is a Caratheodory function under suitable conditions that will be stated in each section.