Title: Comparisons of Green’s functions for families of boundary value problems for higher order differential equations
Speaker: Paul Eloe (University of Dayton)
Abstract: Let $I\subset \mathbb {R}$ be an interval, let $L$ denote a linear ordinary differential operator defined on $C^{n}(I)$ and let $B: C^{n-1}(I)\rightarrow \mathbb{R}^{n}$ be linear. We consider boundary value problems of the form \begin{align*} Ly(x)&=f(x,y(x),\ldots ,y^{(n-1)}(x)), \quad x\in I, \\ By&= c, \end{align*} where $f: I\times \mathbb{R}^{n}$ is continuous. A survey of sign properties and comparison results for Green's functions of families of boundary value problems is given. We shall focus on two point boundary conditions and consider families of boundary value problems that include conjugate type, right focal type and Lidstone type boundary conditions. The talk concludes with current efforts to extend these type of results to two point boundary value problems for fractional differential equations of Riemann-Liouville type.
Seminar URL: https://research.math.osu.edu/aot/
