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

Guglielmo Feltrin; Christophe Troestler

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arXiv · 2405.05664

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

Guglielmo Feltrin·Christophe Troestler

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Abstract

In this paper, we focus our attention on the positive solutions to second-order nonlinear ordinary differential equations of the form $u''+q(t)g(u)=0$, where $q$ is a sign-changing weight and $g$ 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.

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Guglielmo Feltrin, Christophe Troestler. 2024-05-09. Uniqueness, non-degeneracy, and exact multiplicity of positive solutions for superlinear elliptic problems. https://arxiv.org/abs/2405.05664

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