The Hilbert space approach in the theory of differential equations (Adolfo Rumbos, Pomona College)

In this talk we discuss the Hilbert space approach, or the variational approach, in the study of questions of existence and multiplicity for some two-point boundary-value problems for nonlinear, second order, ordinary differential equations (ODEs).  We illustrate the use of the Hilbert space approach in obtaining some old existence results for periodic solutions of a semilinear ODE, and some recent multiplicity results for a related problem. The talk is based on joint work with Noah Benjamin (Pomona College ’23) and Leandro Recôva (Cal Poly Pomona).