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On the Maximum and Minimum of Some Functionals for the Eigenvalue Problem of Sturm-Liouville Type

✍ Scribed by H.H. Chern; C.L. Shen

Publisher
Elsevier Science
Year
1994
Tongue
English
Weight
461 KB
Volume
107
Category
Article
ISSN
0022-0396

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✦ Synopsis

Let (\lambda_{n}(q)) be the (n)th eigenvalue of the Sturm-Liouville equation (y^{\prime \prime}+(\lambda-q(x)) y=0), (y(-l / 2)=y(l / 2)=0). With certain restrictions on the class of functions (q) we determine the shapes of the solutions of the extremal problems for the functionals (\lambda_{n}(q)) and the minimum problem for the functional (\lambda_{2}(q)-\lambda_{1}(q)). 1994 Academic Press, Inc.

📜 SIMILAR VOLUMES

Regularity of the Inversion Problem for
Regularity of the Inversion Problem for the Sturm–Liouville Difference Equation: II. Two-Sided Estimates for the Diagonal Value of the Green Function
✍ N.A. Chernyavskaya; L.A. Shuster 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 117 KB

This is the second part of a study of the inversion for a Sturm-Liouville difference equation. Our main result consists in getting two-sided (sharp by order) estimates for the diagonal value of the Green difference function