On bifurcation for semilinear elliptic Dirichlet problems on shrinking domains

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.

arXiv comment18 pages; survey article based on arXiv:1305.3078 and arXiv:1301.1458