Multiple Positive For A Class Of Singular Quasilinear Elliptic Equations

In this thesis, we deal with the following singular quasilinear elliptic boundary value problem: where Ω is a smooth bounded domain in RN(N≥3),△pu=div(|(?)u|p-2(?)u) is the p-Laplacian,2≤p<N, h, W are continuous functions, r and q are positive constants, λ is the parameter.Since the corresponding functional of (Pλ) fails to be Prechet differentiable, the singular problem(Pλ) becomes more complicated to deal with by using the classical critical point theory. Hence we have to overcome more difficulties in the study of positive solutions for (Pλ). In this thesis, by using the Ekeland variational principle and the Nehari manifold method, we overcome the above difficulties and show that (Pλ) has at least two positive solutions.