On bifurcation for semilinear elliptic Dirichlet problems and the Morse-Smale index theorem
Analysis of PDEs
2013-10-07 v3 Functional Analysis
Spectral Theory
Abstract
We study bifurcation from a branch of trivial solutions of semilinear elliptic Dirichlet boundary value problems on star-shaped domains, where the bifurcation parameter is introduced by shrinking the domain. In the proof of our main theorem we obtain in addition a special case of an index theorem due to S. Smale.
Keywords
Cite
@article{arxiv.1301.1458,
title = {On bifurcation for semilinear elliptic Dirichlet problems and the Morse-Smale index theorem},
author = {Alessandro Portaluri and Nils Waterstraat},
journal= {arXiv preprint arXiv:1301.1458},
year = {2013}
}
Comments
6 pages; v2: all results improved from balls to star-shaped domains; v3: final version, accepted for publication in J. Math. Anal. Appl