有界柱体中的半线性方程：Morse 指数与从一维解分岔
偏微分方程分析
2024-08-15 v2
摘要
本文研究具有自然一类仅依赖于一个变量且其简单几何反映区域几何结构的解的域上的半线性椭圆方程。我们证明在相当一般的假设下，其他类型的解也存在。更确切地说，我们考虑有界柱体中的一维解，并将合适的变量分离与常微分方程理论相结合，展示如何计算此类解的 Morse 指数。该 Morse 指数随后被用于证明局部与全局分岔结果。
引用
@article{arxiv.2311.15236,
title = {Semilinear equations in bounded cylinders: Morse index and bifurcation from one-dimensional solutions},
author = {Danilo Gregorin Afonso},
journal= {arXiv preprint arXiv:2311.15236},
year = {2024}
}
备注
In this new version, we have extended and improved the results of the first one. Most notably, we now deal with both positive and sign-changing solutions, and obtain both local and global bifurcation results. Comments are appreciated!