Global structure of solutions for a class of two-point boundary value problems involving singular and convex or concave nonlinearities

This paper investigates the following two-point singular boundary value problems (BVP): ⎧⎨⎩ −x (t) = λxq +xp, t∈ (0, 1), x(t)>0, t∈ (0, 1), x(0) = x(1) = 0, where q <0 and p >0 are fixed given numbers; λ ∈ R+ = [0,+∞) is a parameter. The results obtained are the global structure of solutions and exact number of solutions when p 1 orp >1 and q is sufficiently small. © 2005 Elsevier Inc. All rights reserved.