Applied Maths Seminar: Santra -- Asymptotic behavior of radial solutions of a semilinear elliptic PDE in an annulus by Morse Index

We discuss the asymptotic behavior of radial solutions for semilinear elliptic PDE with
Dirichlet boundary conditions in an annulus.  We are able to show that Morse Index
information on such solutions provide the complete blow up behavior.  In particular we
obtain that the radial ground state solutions blow up and concentrates at the
inner/outer boundary of the annulus.