Traces and inverse nodal problem for Sturm-Liouville operators with frozen argument (Q2184907)

The Sturm-Lioville equation \[ -y''(x)+q(x)y(a)=\lambda y(x),\; 0<x<\pi, \] with a frozen argument is studied; here $a\in(0,\pi)$. Trace formulas are derived, and the solution of the inverse nodal problem is provided.