The Gel'fand problem for the biharmonic operator

Abstract

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

Cited by in corpus (12)

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• Remarks on two fourth order elliptic problems in whole space
• Classification of finite Morse index solutions of higher-order Gelfand-Liouville equation
• Embeddings of weighted Sobolev spaces and a weighted fourth order elliptic equation
• On stable and finite Morse index solutions of the fractional Toda system
• Qualitative properties of Hénon type equations with exponential nonlinearity
• Classification of stable solutions to a non-local Gelfand-Liouville equation
• Existence of stable solutions to $(-\Delta {)}^{m}u=e^u$ in ${\mathbb{R}}^N$ with $m\ge 3$ and $N>2m$
• The Hölder Quasicontinuity for Riesz-Morrey Potentials and Lane-Emden Equations
• On stable and finite Morse index solutions of the nonlocal Hénon-Gelfand-Liouville equation
• Regularity of extremal solutions of semilinaer fourth-order elliptic problems with general nonlinearities
• Liouville type theorems for stable solutions of the weighted elliptic system