Special Session 34: Variational methods for discrete and continuous boundary value problems (with applications)
Contents
We study existence of positive and compact support solutions to a class of
semilinear elliptic equations related with nonlinear Schr\"{o}dinger equations.
First we prove existence of non-negative solutions by using a Nehari manifold
argument. We also prove that solutions are actually positive for a bounded interval
of values of a parameter and then study the existence of compact support
solutions with the help of a Pohozaev identity. Bifurcation at infinity and the
asymptotic behavior of the solution branches are studied as well.
This is joint work with J.I.D\'{i}az and Y. Ilyasov.