次线性泛函与Volterra微分方程的增长率
Growth Rates of Sublinear Functional and Volterra Differential Equations
摘要：
研究了一类非线性泛函和Volterra微分方程正解的增长率。假设方程是自治的（或渐近自治的），并且非线性相关性的增长速度低于任何线性函数。我们施加额外的正则性的函数渐近这个非线性函数，而不是非线性本身。本文的主要结果表明，解的增长率可以通过确定一个平凡泛函微分方程（FDE）的增长率得到，该方程具有相同的非线性度，其所有相关测度都集中在零，平凡FDE是一个自治的非线性常微分方程.我们还提供了直接的渐近信息的解决方案的FDE在额外的条件下的非线性，并利用正则变分理论的锐化和扩展的结果。
英文摘要：
This paper considers the growth rates of positive solutions of scalar nonlinear functional and Volterra differential equations. The equations are assumed to be autonomous (or asymptotically so), and the nonlinear dependence grows less rapidly than any linear function. We impose extra regularity properties on a function asymptotic to this nonlinear function, rather than on the nonlinearity itself. The main result of the paper demonstrates that the growth rate of the solution can be found by determining the rate of growth of a trivial functional differential equation (FDE) with the same nonlinearity and all its associated measure concentrated at zero; the trivial FDE is nothing other than an autonomous nonlinear ODE. We also supply direct asymptotic information about the solution of the FDE under additional conditions on the nonlinearity, and exploit the theory of regular variation to sharpen and extend the results.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
