Báo Cáo Báo cáo hóa học MULTIPLE POSITIVE SOLUTIONS OF SINGULAR p-LAPLACIAN PROBLEMS BY VARIATIONAL METHODS

MULTIPLE POSITIVE SOLUTIONS OF SINGULAR p-LAPLACIAN PROBLEMS BY VARIATIONAL METHODS KANISHKA PERERA AND ZHITAO ZHANG Received 20 July 2004 We obtain multiple positive solutions of singular p-Laplacian problems using variational methods. The techniques are applicable to other types of singular problems as well. 1. Introduction We consider the singular quasilinear elliptic boundary value problem ư∆ p u = a(x)uưγ + λ f (x,u) in Ω, (1.1) u 0 in Ω, u = 0 on ∂Ω, where Ω is a bounded C 2 domain in Rn ,n ≥ 1, ∆ p u = div(|∇u| pư2 ∇u) is the p-Laplacian, 1 0 is a constant, λ 0 is a parameter, and f is a Carath´ odory function on Ω × [0, ∞) satisfying e (x,t)∈Ω×[0,T] sup f (x,t) 0. (1.2) The semilinear case p = 2 with