Three positive solutions of N-dimensional p-Laplacian with indefinite weight

摘要

This paper is concerned with the global behavior of components of positive radial solutions for the quasilinear elliptic problem with indefinite weight div(?p(?u)) + λh(x)f(u) = 0, in B, u = 0, on ?B, where ?p(s) = |s| p?2 s, B is the unit open ball of RN with N ≥ 1, 1 < p < ∞, λ > 0 is a parameter, f ∈ C([0, ∞), [0, ∞)) and h ∈ C(Bˉ) is a sign-changing function. We manage to determine the intervals of λ in which the above problem has one, two or three positive radial solutions by using the directions of a bifurcation.