Mathematical Sciences: Bifurcation From Infinity for Semilinear Elliptic Partial Differential Equations: The Influence of Nonlinear Growth and Domain Geometry

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The principal investigator will use bifurcation from infinity techniques to study the asymptotic behavior of bifurcating branches of solutions of semilinear elliptic equations to get detailed information about the existence and multiplicity of solutions for such problems as well as stability information for the associated time-evolution problems. Solution structure is strongly dependent on the spatial dimension and the geometry of the domain. The stability of steady state solutions in the case where multiple solutions exist is extemely delicate and important in most physical situations.