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Morse index and symmetry breaking for an elliptic equation with negative exponent in expanding annuli

Part of: Elliptic equations and systems

Published online by Cambridge University Press:  14 August 2017

Zongming Guo ,
Linfeng Mei  and
Zhitao Zhang
Zongming Guo
Affiliation:
Department of Mathematics, Henan Normal University, Xinxiang 453007, People's Republic of China (gzm@htu.cn; mlf@htu.edu.cn)
Linfeng Mei
Affiliation:
Department of Mathematics, Henan Normal University, Xinxiang 453007, People's Republic of China (gzm@htu.cn; mlf@htu.edu.cn)
Zhitao Zhang
Affiliation:
Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, People's Republic of China (zzt@math.ac.cn)
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Extract

Bifurcation of non-radial solutions from radial solutions of a semilinear elliptic equation with negative exponent in expanding annuli of ℝ2 is studied. To obtain the main results, we use a blow-up argument via the Morse index of the regular entire solutions of the equation

The main results of this paper can be seen as applications of the results obtained recently for finite Morse index solutions of the equation

with N ⩾ 2 and p > 0.

Keywords

expanding annulibifurcationsymmetry breakingnegative exponentMorse index

MSC classification

Secondary: 35J25: Boundary value problems for second-order elliptic equations 35J61: Semilinear elliptic equations 35J60: Nonlinear elliptic equations
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 147 , Issue 6 , December 2017 , pp. 1215 - 1232
Copyright
Copyright © Royal Society of Edinburgh 2017 

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