We study a class of nonlinear eigenvalue problems which involves a convolution operator as well as a superlinear nonlinearity. Our variational existence proof is based on constrained optimization and provides a one-parameter family of solutions with positive eigenvalues and unimodal eigenfunctions. We also discuss the decay properties and the numerical computations of those eigenfunctions, and conclude with two asymptotic results concerning small and large eigenvalues.

中文翻译：

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非线性和非局部特征值问题：变分存在、衰减特性、近似和通用标度限制

我们研究一类涉及卷积算子和超线性非线性的非线性特征值问题。我们的变分存在证明基于约束优化，并提供具有正特征值和单峰特征函数的单参数解决方案系列。我们还讨论了这些特征函数的衰减特性和数值计算，并以关于小特征值和大特征值的两个渐近结果作为结论。