تقرير
Uniqueness, non-degeneracy, and exact multiplicity of positive solutions for superlinear elliptic problems
| العنوان: | Uniqueness, non-degeneracy, and exact multiplicity of positive solutions for superlinear elliptic problems |
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| المؤلفون: | Feltrin, Guglielmo, Troestler, Christophe |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Analysis of PDEs, 34B08, 34B15, 34B18, 34C23 |
| الوصف: | 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. Comment: 24 pages, 11 figures |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2405.05664 |
| رقم الأكسشن: | edsarx.2405.05664 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |