On bifurcation for semilinear elliptic Dirichlet problems and the Morse-Smale index theorem

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.

6 pages; v2: all results improved from balls to star-shaped domains; v3: final version, accepted for publication in J. Math. Anal. Appl