A Morse-Smale index theorem for indefinite elliptic systems and bifurcation

被引：12
|
作者：
Portaluri, Alessandro [1 ]
Waterstraat, Nils [2 ]
机构：
[1] Univ Turin, Dept Agr Forest & Food Sci, I-10095 Grugliasco, TO, Italy
[2] Humboldt Univ, Inst Math, D-10099 Berlin, Germany
来源：
JOURNAL OF DIFFERENTIAL EQUATIONS | 2015年 / 258卷 / 05期
关键词：
SPECTRAL FLOW; DIRICHLET PROBLEMS; CRITICAL-POINTS; MASLOV INDEX; FUNCTIONALS; GEODESICS;
D O I：
10.1016/j.jde.2014.11.010
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We generalise the semi-Riemannian Morse index theorem to non-degenerate elliptic systems of partial differential equations on star-shaped domains. Moreover, we apply our theorem to bifurcation from a branch of trivial solutions of semilinear systems, where the bifurcation parameter is introduced by shrinking the domain to a point. This extends recent results of the authors for scalar equations. (C) 2014 Elsevier Inc. All rights reserved.
引用
收藏
页码：1715 / 1748
页数：34
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