Global structure of solutions for a class of two-point boundary value problems involving singular and convex or concave nonlinearities (Q2497383)

The author considers the exact number of positive solutions and the global behavior of the positive solutions of the singular boundary value problem \[ -x''=\lambda x^q+x^p, \qquad x(0)=x(1)=0, \] where \(q<0\) and \(p>0\) are two constants and \(\lambda\in [0,\infty)\) is a parameter. For related results, see \textit{A. Ambrosetti, H. Brézis} and \textit{G. Cerami} [J. Funct. Anal. 122, No. 2, 519--543 (1994; Zbl 0805.35028)].