Abstract

In this paper, we investigate the existence of solutions for a second-order differential inclusion with nonlocal boundary conditions. To establish the existence results for the given problem, first, we apply Schaefer’s fixed point theorem combined with a selection theorem of Bressan and Colombo. Secondly, our result is based on the Covitz–Nadler fixed point theorem for multivalued maps. An example is given to illustrate the obtained results.

中文翻译：

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具有非局部边界条件的二阶非线性微分包含的存在性结果

摘要

在本文中，我们研究了具有非局部边界条件的二阶微分包含解的存在性。为了建立给定问题的存在性结果，首先，我们将 Schaefer 不动点定理与 Bressan 和 Colombo 的选择定理相结合。其次，我们的结果基于多值地图的 Covitz-Nadler 不动点定理。给出一个例子来说明得到的结果。