Eigenvalues for Radially Symmetric Fully Nonlinear Operators
Eigenvalues for Radially Symmetric Fully Nonlinear Operators
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DOI：
10.1080/03605301003674848
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发表时间：
2010-08
影响因子：
1.9
通讯作者：
M. Esteban;P. Felmer;A. Quaas
中科院分区：
文献类型：
--
作者：
M. Esteban;P. Felmer;A. Quaas
本文给出了完全非线性径向对称1-齐次算子特征值存在性的一个初等理论。在粘度解的框架下，存在1-齐次全非线性算子的第一特征值和特征函数的一般理论。这里我们想要证明，对于径向对称算子，或者在一维情况下，可以建立一个更简单的理论，基于阶和度理论的论点。我们得到了以0个数为特征的特征值和特征函数的完备集。
In this paper we present an elementary theory about the existence of eigenvalues for fully nonlinear radially symmetric 1-homogeneous operators. A general theory for first eigenvalues and eigenfunctions of 1-homogeneous fully nonlinear operators exists in the framework of viscosity solutions. Here we want to show that for the radially symmetric operators or in the one dimensional case a much simpler theory, based on ode and degree theory arguments, can be established. We obtain the complete set of eigenvalues and eigenfunctions characterized by the number of zeroes.