Limit-point and limit-circle criteria for Sturm-Liouville equations with intermittently negative principal coefficients

DOI10.1017/S0308210500018874zbMath0635.34021OpenAlexW2125747639MaRDI QIDQ3774177

Ian W. Knowles, Thomas T. Read, W. Norrie Everitt

Publication date: 1986

Published in: Proceedings of the Royal Society of Edinburgh: Section A Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0308210500018874

zbMATH Keywords

limit-pointCaratheodory solutionslimit-circle criteriaSturm- Liouville equations

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15) Eigenvalue problems for integral equations (45C05) Ordinary differential operators (34L99)

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Cites Work

• The essential self-adjointness of Schrödinger-type operators
• On essential self-adjointness for singular elliptic differential operators
• On stability conditions for second order linear differential equations
• On solutions of a differential equation which are not of integrable square
• On the essential self-adjointness of powers of Schrödinger operators
• Self-Adjointness and Spectra of Sturm-Liouville Operators.
• On the number ofL²-solutions of second order linear differential equations
• 11.—Limit-n Criteria of Integral Type
• Interval Limit-Point Criteria for Differential Expressions and their Powers
• ON NECESSARY AND SUFFICIENT CONDITIONS FOR THE EXISTENCE OF CARATHÉODORY SOLUTIONS OF ORDINARY DIFFERENTIAL EQUATIONS
• A Limit-Point Criterion for Expressions with Intermittently Positive Coefficients
• On a Limit-Point Method of Hartman
• Note on the Uniqueness of the Green'S Functions Associated With Certain Differential Equations