A counterexample to a nonlinear version of the Krein-Rutman theorem by R. Mahadevan

A Generalized Krein-Rutman Theorem

A generalized Krein-Rutman theorem for a strongly positive bounded linear operator whose spectral radius is larger than essential spectral radius is established: the spectral radius of the operator is an algebraically simple eigenvalue with strongly positive eigenvector and other eigenvalues are less than the spectral radius.

A Note on the Krein-Rutman Theorem for Sectorial Operators

In this note we present some generalized versions of the Krein-Rutman theorem for sectorial operators. They are formulated in a fashion that can be easily applied to elliptic operators. Another feature of these generalized versions is that they contain some information on the generalized eigenspaces associated with non-principal eigenvalues, which are helpful in the study of the dynamics of evolution equations in ordered Banach spaces.

Perron-Frobenius理论的动力学方法及广义Krein-Rutman型定理

A Dynamical Approach to the Perron-Frobenius Theory and Generalized Krein-Rutman Type Theorems

本文利用线性常微分方程的基本知识提出一种自包含的动力学方法研究经典Perron-Frobenius理论，并据此建立其复版本及证明广义Krein-Rutman型定理。

A note on a non-linear Krein-Rutman theorem

In this note we will present an extension of the Krein-Rutman theorem for an abstract nonlinear, compact, positively 1-homogeneous, monotone non-decreasing operators on a Banach space and apply the result to many nonlinear elliptic partial differential operators.

关于克雷因-鲁曼定理及其后续内容

On the Krein-Rutman theorem and beyond

本文重新审视了克雷因-鲁曼理论，提供了关于正算子中特征值问题和特征向量稳定性的一般结果与构造性估计，并通过多种微分和积分算子的例子进行了说明。

On the Existence of Unstable Bumps in Neural Networks

We study the neuronal field equation, a nonlinear integro-differential equation of Hammerstein type. By means of the Amann three fixed point theorem we prove the existence of bump solutions to this equation. Using the Krein-Rutman theorem we show their Lyapunov instability.