Stable solutions of $-\Delta u = f(u)$ in $\R^N$

TL;DR

This paper establishes Liouville-type theorems for stable solutions of semilinear elliptic equations in the entire Euclidean space, including cases where stability holds outside a compact set, advancing understanding of solution behavior.

Contribution

It provides new Liouville-type results for stable solutions of semilinear elliptic PDEs with convex nonlinearities, extending to solutions stable outside compact sets.

Findings

Liouville-type theorems for stable solutions in alculus

Extensions to solutions stable outside compact sets

Enhanced understanding of solution stability in alculus

Abstract

The paper proves Liouville-type results for stable solutions of semilinear elliptic PDEs with convex nonlinearity, posed on the entire Euclidean space. Extensions to solutions which are stable outside a compact set are also presented.