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<0q<0 and p>0p>0 are fixed given numbers; λ∈R+=[0,+∞)λ∈R+=[0,+∞) is a parameter. The results obtained are the global structure of solutions and exact number of solutions when p⩽1p⩽1 or p>1p>1 and q is sufficiently small.