English

An existence theorem for elliptic equations with nonlocal boundary conditions

Analysis of PDEs 2026-03-16 v1

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.

Keywords

Cite

@article{arxiv.2603.12835,
  title  = {An existence theorem for elliptic equations with nonlocal boundary conditions},
  author = {Chiun-Chang Lee},
  journal= {arXiv preprint arXiv:2603.12835},
  year   = {2026}
}