论微分夹杂的非线性边界问题

Pub Date : 2023-12-29 DOI:10.1134/s00122661230110010

A. V. Arutyunov, Z. T. Zhukovskaya, S. E. Zhukovskiy

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引用次数: 0

摘要

摘要我们考虑了具有非线性边界条件的自治微分夹杂，得到了这些夹杂在绝对连续函数类中解存在的充分条件。结果表明，相应的存在定理适用于 Cauchy 问题和反周期边界值问题。该结果用于推导连续可微分函数的新均值不等式。

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On Nonlinear Boundary Value Problems for Differential Inclusions

Abstract

We consider autonomous differential inclusions with nonlinear boundary conditions. Sufficient conditions for the existence of solutions in the class of absolutely continuous functions are obtained for these inclusions. It is shown that the corresponding existence theorem applies to the Cauchy problem and the antiperiodic boundary value problem. The result is used to derive a new mean value inequality for continuously differentiable functions.

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