שמור ב:
| Main Authors: | , , |
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| פורמט: | Preprint |
| יצא לאור: |
2024
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| נושאים: | |
| גישה מקוונת: | https://arxiv.org/abs/2402.19084 |
| תגים: |
הוספת תג
אין תגיות, היה/י הראשונ/ה לתייג את הרשומה!
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תוכן הענינים:
- In this paper we consider a superlinear one-dimensional elliptic boundary value problem that generalizes the one studied by Moore and Nehari in [43]. Specifically, we deal with piecewise-constant weight functions in front of the nonlinearity with an arbitrary number $κ\geq 1$ of vanishing regions. We study, from an analytic and numerical point of view, the number of positive solutions, depending on the value of a parameter $λ$ and on $κ$. Our main results are twofold. On the one hand, we study analytically the behavior of the solutions, as $λ\downarrow-\infty$, in the regions where the weight vanishes. Our result leads us to conjecture the existence of $2^{κ+1}-1$ solutions for sufficiently negative $λ$. On the other hand, we support such a conjecture with the results of numerical simulations which also shed light on the structure of the global bifurcation diagrams in $λ$ and the profiles of positive solutions. Finally, we give additional numerical results suggesting that the same high multiplicity result holds true for a much larger class of weights, also arbitrarily close to situations where there is uniqueness of positive solutions.