existence of solutions for a class of singular quasilinear elliptic resonance problems

the paper concerns a resonance problem for a class of singular quasilinear elliptic equations in weighted sobolev spaces. the equation set studied is one of the most useful sets of navier–stokes equations; these describe the motion of viscous fluid substances such as liquids, gases and so on. by using galerkin-type techniques, the brouwer fixed point theorem, and a new weighted compact sobolev-type embedding theorem established by shapiro, we show the existence of a nontrivial solution.