With A Critical Sobolev And Hardy Exponents Quasilinear Dirichlet Problem For The Infinite And Varied Number Existence Of Solutions

In this paper, by constructing invariant sets of descending flow, we use variationalmethod to study existence of infinitely many nodal solutions for the p-Laplacian equation involving Hardy-Sobolev subcritical singular and non-singular termswhereλandμare two positive parameters andΩ(?)Rⁿ is a bounded domain with smooth boundary (?)Ωand contains 0 in its interior,△_pu = div(|▽u|^p-2▽u) is the p-Laplacian operator. We assume throughout that : 1 < p < n, 0≤s < p, p≤q< p^*(s) = (n-s)/(n-p)p, p≤r * = p^*(0) = np/n-p.