The Gel'fand problem for the biharmonic operator

TL;DR

This paper investigates stable solutions to a fourth order nonlinear elliptic equation, focusing on their properties in both unbounded and bounded domains, contributing to the understanding of higher-order elliptic problems.

Contribution

It provides new insights into the behavior of stable solutions for the Gel'fand problem involving the biharmonic operator in various domain settings.

Findings

Characterization of stable solutions in entire space

Analysis of solutions in bounded domains

New stability criteria for fourth order equations

Abstract

We study stable solutions of a fourth order nonlinear elliptic equation, both in entire space and in bounded domains.