Existence of stable solutions to $(-Δ)^m u=e^u$ in $\mathbb{R}^N$ with $m \geq 3$ and $N > 2m$

preprint2015arXivOpen access

We consider the polyharmonic equation $(-Δ)^m u=e^u$ in $\mathbb{R}^N$ with $m \geq 3$ and $N > 2m$ . We prove the existence of many entire stable solutions. This answer some questions raised by Farina and Ferrero.

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Existence of stable solutions to $(-Δ)^m u=e^u$ in $\mathbb{R}^N$ with $m \geq 3$ and $N > 2m$

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Existence of stable solutions to (−Δ)mu=eu(-Δ)^m u=e^u(−Δ)mu=eu in RN\mathbb{R}^NRN with m≥3m \geq 3m≥3 and N>2mN > 2mN>2m

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Existence of stable solutions to $(-Δ)^m u=e^u$ in $\mathbb{R}^N$ with $m \geq 3$ and $N > 2m$