论文标题
简单的超线性特征值问题的独特结果
A uniqueness result for a simple superlinear eigenvalue problem
论文作者
论文摘要
我们研究了双线性本构定律的特征卷积运算符的特征值问题，并在拓扑形状约束下建立了单参数非线性本征函数家族的存在和唯一性。我们的证明使用标量参数的非线性更改，并将Krein-Rutmann参数应用于线性替代问题。我们还提供数值模拟，并讨论两种限制案例的渐近学。
We study the eigenvalue problem for a superlinear convolution operator in the special case of bilinear constitutive laws and establish the existence and uniqueness of a one-parameter family of nonlinear eigenfunctions under a topological shape constraint. Our proof uses a nonlinear change of scalar parameters and applies Krein-Rutmann arguments to a linear substitute problem. We also present numerical simulations and discuss the asymptotics of two limiting cases.
