Waterstraat, Nils
(2015)
On bifurcation for semilinear elliptic Dirichlet problems on shrinking
domains.
In: Escher, Joachim and Schrohe, Elmar and Seiler, Joerg and Walker, Christoph, eds.
Elliptic and Parabolic Equations.
Springer Proceedings in Mathematics & Statistics
(119).
Springer, Cham, pp. 273-291.
ISBN 978-3-319-12546-6.
Abstract
We consider the Dirichlet problem for semilinear elliptic equations on a bounded domain which is diffeomorphic to a ball and investigate bifurcation from a given (trivial) branch of solutions, where the radius of the ball serves as bifurcation parameter. Our methods are based on well known results from
variational bifurcation theory, which we outline in a separate section for the readers' convenience.
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