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

## March 23 @ 4:30 pm - 5:30 pm

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).