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arXiv · 2603.12835

An existence theorem for elliptic equations with nonlocal boundary conditions

Chiun-Chang Lee
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Abstract

The focus of this study is on exploring some qualitative properties of solutions to a class of semilinear elliptic problems in bounded domains, where the boundary conditions depend non-locally on the unknown solution at specified interior points and its integral. The primary approach integrates a fixed-point argument with refined asymptotic estimates to establish the existence and structure of solutions. Furthermore, the maximum principles are established under practical nonlocal-type boundary conditions.

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Chiun-Chang Lee. 2026-03-13. An existence theorem for elliptic equations with nonlocal boundary conditions. https://doi.org/10.1016/j.bulsci.2025.103768

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