A criterion for correct solvability of the Sturm-Liouville equation in the space 𝐿_{𝑝}(𝑅)

DOI10.1090/S0002-9939-01-06145-7zbMath0994.34014OpenAlexW1581231416MaRDI QIDQ2781251

L. A. Shuster, N. A. Chernyavskaya

Publication date: 19 March 2002

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9939-01-06145-7

zbMATH Keywords

Sturm-Liouville equationcorrect solvability

Mathematics Subject Classification ID

General theory of ordinary differential operators (47E05) Growth and boundedness of solutions to ordinary differential equations (34C11) Special ordinary differential equations (Mathieu, Hill, Bessel, etc.) (34B30) Boundary value problems on infinite intervals for ordinary differential equations (34B40)

Related Items (12)

Criteria for correct solvability of a general Sturm-Liouville equation in the space \(L_1(\mathbb R)\) ⋮ Correct solvability of the Sturm-Liouville equation with delayed argument ⋮ A limit-point criterion for a class of Sturm-Liouville operators defined in 𝐿^{𝑝} spaces ⋮ Spaces admissible for the Sturm-Liouville equation ⋮ An embedding theorem ⋮ An embedding theorem for a weighted space of Sobolev type and correct solvability of the Sturm-Liouville equation ⋮ Correct solvability, embedding theorems and separability for the Sturm-Liouville equation ⋮ On the speed at which solutions of the Sturm-Liouville equation tend to zero ⋮ Regularity of the inversion problem for the Sturm-Liouville difference equation III. A criterion for regularity of the inversion problem ⋮ Regularity of the inversion problem for the Sturm-Liouville difference equation IV. Stability conditions for a three-point difference scheme with non-negative coefficients ⋮ Stability and absolute stability of a three-point difference scheme ⋮ Methods of analysis of the condition for correct solvability in L p (ℝ) of general Sturm-Liouville equations

Cites Work

• Solvability in \(L_p\) of the Dirichlet problem for a singular nonhomogeneous Sturm-Liouville equation
• Conformally flat Riemannian metrics, Schrödinger operators, and semiclassical approximation
• Estimates for the Green function of a general Sturm-Liouville operator and their applications
• Asymptotics on the Diagonal of the Green Function of a Sturm-Liouville Operator and its Applications

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