Morse indices and symmetry breaking for the Gelfand equation in expanding annuli

Linfeng Mei; Zongming Guo

doi:10.3934/dcdsb.2017072

Article Contents

2017, Volume 22, Issue 4: 1509-1523. Doi: 10.3934/dcdsb.2017072

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Morse indices and symmetry breaking for the Gelfand equation in expanding annuli

Linfeng Mei^, and
Zongming Guo

Department of Mathematics, Henan Normal University, Xinxiang 453007, China

* Corresponding author
* Corresponding author

Received: January 31, 2016

Revised: October 31, 2016

Published: August 2017

The research of the first author is supported by NSFC (11371117) and Startup Fund for Doctors of Henan Normal University (qd14154); the research of the second author is supported by NSFC (11171092, 11571093).

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Abstract

Bifurcation of nonradial solutions from radial solutions of

$-Δ u=λ e^u$

in expanding annuli of ${\mathbb{R}^N}$ with $3 ≤q N ≤q 9$ is studied. To obtain the main results, we use a blow-up argument via Morse indices of the regular entire solutions of (0.1).

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Mathematics Subject Classification: Primary:35K20, 35R35;Secondary:35J60.

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References

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