On Perturbative Hardy-Type Inequalities
Given a three-coefficient Sturm–Liouville differential expression $\tau_0 = r_0^{-1}[-(d/dx)p_0(d/dx)+q_0]$ and its perturbation $\tau_{q_1}=\tau_0+r_0q^{-1}$ on an interval $(a,b)\subset\mathbb{R}$, we employ the existence of a strictly positive solution $u_0(\lambda_0,\cdot)>0$ on $(a,b)$ o...
Saved in:
| Date: | 2023 |
|---|---|
| Main Authors: | , , |
| Format: | Article |
| Language: | English |
| Published: |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна Національної академії наук України
2023
|
| Subjects: | |
| Online Access: | https://jmag.ilt.kharkiv.ua/index.php/jmag/article/view/999 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Journal Title: | Journal of Mathematical Physics, Analysis, Geometry |
Institution
Journal of Mathematical Physics, Analysis, Geometry| Summary: | Given a three-coefficient Sturm–Liouville differential expression $\tau_0 = r_0^{-1}[-(d/dx)p_0(d/dx)+q_0]$ and its perturbation $\tau_{q_1}=\tau_0+r_0q^{-1}$ on an interval $(a,b)\subset\mathbb{R}$, we employ the existence of a strictly positive solution $u_0(\lambda_0,\cdot)>0$ on $(a,b)$ of $\tau_0u_0=\lambda_0u_0$ to derive a quadratic form inequality for $\tau_{q_1}$ that naturally generalizes the well-known Hardy inequality and reduces to it in the particular case $p_0=r_0=u_0(0,\cdot)=1$, $q_0=\lambda_0=0$, $a\in \mathbb{R}, b=\infty.$
Mathematical Subject Classification 2020: 34A40, 34B24, 34C10, 47E05,26D20, 34L05 |
|---|