On Multiple Solutions For A Class Of Singular Elliptic Equations

In this paper, we focus on the multiple solutions of a class of singular elliptic boundary value problems as follows where Ω is a smooth bounded domain in RN(N≥3),2≤p <N,0∈Ω,0≤μ<μp,μp=(N—p)p/pp is the best constant of the Hardy inequality,△pu=div(|▽-u|p-2▽u) is p-Laplacian, λ>0is a parameter, f(u) is a perturbation satis-fying some suitable conditions.In the semilinear case, that is, p=2for the problem (ppμ,λ), by using variational methods and a Ricceri’s three-critical points theorem, we prove that the problem (pμ2,λ) has at least three weak solutions when f(u) satisfies sublinear growth condition at infinity; further more, if f(u) is odd with respect to u and f2is an open ball, then by the principle of symmetric criticality we establish the quantity relations between the number of solutions of (pμ2,λ) and the space dimension N.After that, under similar conditions, combining variational methods and some an-alytic techniques, we obtain multiple solutions of the problem (pμp,λ) in the quasilinear form, that is,2<p<N.