Three positive radial solutions for elliptic equations in a ball

In this work we deal with a class of second-order elliptic problems of the form − u = λk(|x |) f (u) in Ω , with non-homogeneous boundary condition u = a on ∂Ω where Ω is the ball of radius R0 centered at origin, λ, a are positive parameters, f ∈ C([0,+∞), [0,+∞)) is an increasing function and k ∈ C([0, R0], [0,+∞)) is not identically zero on any subinterval of [0, R0]. We obtain via a fixed point theorem of cone expansion/compression type the existence of at least three positive radial solutions. © 2005 Elsevier Ltd. All rights reserved. MSC: 35J65; 35J60; 34B18; 47H11