Uniqueness, non‐degeneracy, and exact multiplicity of positive solutions for superlinear elliptic problems

Abstract In this paper, we focus our attention on the positive solutions to second‐order nonlinear ordinary differential equations of the form , where is a sign‐changing weight and is a superlinear function. We exploit the classical shooting approach and the comparison theorem to present non‐degeneracy and exact multiplicity results for positive solutions. This completes the multiplicity results obtained by Feltrin and Zanolin. Numerical examples and some related open problems are also discussed.