| Abstract: |
| In this talk, we present an one dimensional Sobolev-type inequality and use it to obtain the estimates for eigenvalues for even ordered differential equations satisfying periodic and anti periodic boundary conditions. In the higher order periodic case, we introduce suitable moment constraints to eliminate the polynomial kernel, leading to a Sobolev-Poincare
inequalities with explicit scaling. In contrast, anti-periodic conditions naturally yield coercive estimates without additional constraints. These Sobolev-type inequalities provide a unified framework for analyzing boundary value problems and serve as the main tool for deriving further spectral and stability results. |
|