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

页码：1715 / 1748

页数：34

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