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On a singular eigenvalue problem and its applications in computing the Morse index of solutions to semilinear PDE’s
Nonlinear Analysis: Real World Applications ( IF 1.8 ) Pub Date : 2020-03-19 , DOI: 10.1016/j.nonrwa.2020.103133
Anna Lisa Amadori , Francesca Gladiali

We investigate nodal radial solutions to semilinear problems of type Δu=f(|x|,u)inΩ,u=0onΩ,where Ω is a bounded radially symmetric domain of RN (N2) and f is a real function. We characterize both the Morse index and the degeneracy in terms of a singular one dimensional eigenvalue problem, which is studied in full detail. The presented approach also describes the symmetries of the eigenfunctions. This characterization enables to give a lower bound for the Morse index in a forthcoming work.



中文翻译:

关于奇异特征值问题及其在计算半线性PDE解的摩尔斯指数中的应用

我们研究类型为半线性问题的节点径向解 -Δü=F|X|üΩü=0Ω哪里 Ω 是的有界径向对称域 [Rññ2)和 F是一个真正的功能。我们用一个奇异的一维特征值问题来描述摩尔斯指数和简并性,并对其进行了详细的研究。提出的方法还描述了本征函数的对称性。这种表征使得在即将进行的工作中能够给出莫尔斯指数的下限。

更新日期:2020-03-19
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