Work

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

Year: 2026

Type: article

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.

Source: Journal of the London Mathematical Society

DOI: 10.1112/jlms.70476

Authors: Guglielmo Feltrin, Christophe Troestler

Institutions: University of Udine, University of Mons

Language: English

Topic: Nonlinear Differential Equations Analysis

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Istituto Nazionale di Alta Matematica "Francesco Severi", Fonds De La Recherche Scientifique - FNRS, Gruppo Nazionale per l'Analisi Matematica, la Probabilità e le loro Applicazioni, European Research Council

Award: G2495290661