Multiplicity Results for Some Singular Elliptic and Degenerate Elliptic Dirichlet Problems

In this paper we consider the problem —Δ = () + () in Ω, = 0 on , where λ ∈ (0, ∞), Ω is a strictly convex bounded and domain in R with ≥ 2, 1 < < 2, — 1 < < : (0, ∞) → (0, ∞) is a nonincreasing, and locally Lipchitz continuous function (that may be singular at 0) and : [0, ∞) → (0, ∞) is a contnuous and nondecreasing function satisfying inf<0 () > 0, 0 < lim∞ () < ∞. We prove that there exists λ* > 0 such that for 0 < λ < λ* the above problem has at least two positive solutions in Π (Ω) and that λ = 0 is a bifurcation point from infinity. We show that this result remains true for problems of the form − = () + λ () + in Ω, = 0 on ΘΩ for Ω a and bounded domain, 0 ≤ ∈ (Ω), = 2, 1 < < ( + 2) / ( — 2) and with ”locally Lipchitz” replaced by ”continuous”