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

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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

Variational bifurcation
Crossing forms
Morse index theorem
Semilinear elliptic PDE

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