English

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