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February 23, 2026Journal of the London Mathematical Society0 citations

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

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GFGuglielmo FeltrinCTChristophe Troestler

Key Points

  • The central aim is to investigate the uniqueness and multiplicity of positive solutions for specific elliptic problems.
  • Analyzed second-order nonlinear ordinary differential equations with a sign-changing weight and superlinear function.
  • Employed the classical shooting approach and comparison theorem to derive results.
  • Discussed numerical examples and related open problems.
  • Established non-degeneracy of positive solutions for superlinear elliptic problems.
  • Determined exact multiplicity results, completing previous work by Feltrin and Zanolin.

Abstract

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.

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Cite This Study

Feltrin et al. (2026) studied this question.

synapsesocial.com/papers/699ba05e72792ae9fd86fc22https://doi.org/10.1112/jlms.70476
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