Classification and Liouville-type theorems for semilinear elliptic equations in unbounded domains

TL;DR

This paper classifies stable and finite Morse index solutions to semilinear elliptic equations in Euclidean space and certain unbounded domains, providing insights into their structure and stability properties.

Contribution

It offers a comprehensive classification of solutions in dimensions up to 10 and in specific unbounded domains, extending existing results in elliptic PDE theory.

Findings

Classification of stable solutions in dimensions ≤10

Results on solutions in certain unbounded domains

Insights into Morse index and stability properties

Abstract

We classify stable and finite Morse index solutions to general semilinear elliptic equations posed in Euclidean space of dimension at most 10, or in some unbounded domains.