Conditions for the Existence of Conjugate Points for a Fourth Order Linear Differential Equation

Abstract

Previous article Next article Full AccessConditions for the Existence of Conjugate Points for a Fourth Order Linear Differential EquationJohn S. BradleyJohn S. Bradleyhttps://doi.org/10.1137/0117086PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] Dallas Banks, Bounds for the eigenvalues of some vibrating systems, Pacific J. Math., 10 (1960), 439–474 MR0117378 0097.16501 CrossrefGoogle Scholar[2] John H. Barrett, Two-point boundary problems for linear self-adjoint differential equations of the fourth order with middle term, Duke Math. J., 29 (1962), 543–554 10.1215/S0012-7094-62-02955-1 MR0148981 0108.08204 CrossrefISIGoogle Scholar[3] E. S. Čičkin, A non-oscillation theorem for a linear self-adjoint differential equation of fourth order, Izv. Vysš. Učebn. Zaved. Matematika, 1960 (1960), 206–209 MR0137900 Google Scholar[4] A. M. Fink, The functional T$\int \sb{0}\sp{T}$R and the zeroes of a second order linear differential equation, J. Math. Pures Appl. (9), 45 (1966), 387–394 MR0208053 0144.09402 Google Scholar[5] A. M. Fink, On the zeros of $y\sp{\prime\prime}+py=0$ with linear, convex and concave p, J. Math. Pures Appl. (9), 46 (1967), 1–10 MR0213651 0153.11401 Google Scholar[6] Don B. Hinton, Clamped end boundary conditions for fourth-order selfadjoint differential equations, Duke Math. J., 34 (1967), 131–138 10.1215/S0012-7094-67-03415-1 MR0208054 0148.06402 CrossrefISIGoogle Scholar[7] Walter Leighton, On the zeros of solutions of a second-order linear differential equation, J. Math. Pures Appl. (9), 44 (1965), 297–310 MR0186868 0128.30803 Google Scholar[8] Walter Leighton, Erratum: “On the zero of solutions of a second-order linear differential equation”, J. Math. Pures Appl. (9), 46 (1967), 10– MR0214856 0189.37401 Google Scholar[9] Walter Leighton and , Zeev Nehari, On the oscillation of solutions of self-adjoint linear differential equations of the fourth order, Trans. Amer. Math. Soc., 89 (1958), 325–377 MR0102639 0084.08104 CrossrefGoogle Scholar[10] A. Ju. Levin, Distribution of the zeros of solutions of a linear differential equation, Soviet Math. Dokl., 5 (1964), 818–821 0117.05003 Google Scholar[11] L. D. Nikolenko, Some criteria for non-oscillation of a fourth order differential equation, Dokl. Akad. Nauk SSSR (N.S.), 114 (1957), 483–485 MR0091394 0079.11101 Google Scholar[12] William T. Reid, Riccati matrix differential equations and non-oscillation criteria for associated linear differential systems, Pacific J. Math., 13 (1963), 665–685 MR0155049 0119.07401 CrossrefISIGoogle Scholar[13] Thomas L. Sherman, Properties of solutions of $n{\rm th}$ order linear differential equations, Pacific J. Math., 15 (1965), 1045–1060 MR0185185 0132.31204 CrossrefISIGoogle Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails Lyapunov-Type Inequalities for Higher-Order Linear Differential EquationsLyapunov Inequalities and Applications | 28 January 2021 Cross Ref Existence of conjugate points for second and fourth order differential equationsProceedings of the Royal Society of Edinburgh: Section A Mathematics, Vol. 89, No. 3-4 | 14 November 2011 Cross Ref The existence of conjugate points for selfadjoint differential equations of even orderProceedings of the American Mathematical Society, Vol. 56, No. 1 | 1 January 1976 Cross Ref Green's function for n-n boundary value problem and an analogue of Hartman's resultJournal of Mathematical Analysis and Applications, Vol. 51, No. 3 | 1 Sep 1975 Cross Ref Separation Theorems for Self-Adjoint Linear Differential Equations of the Fourth OrderWilliam Brunner MillerSIAM Journal on Mathematical Analysis, Vol. 6, No. 4 | 17 February 2012AbstractPDF (1582 KB)Bounds for Eigenvalues and Conditions for Existence of Conjugate PointsD. O. BanksSIAM Journal on Applied Mathematics, Vol. 27, No. 3 | 12 July 2006AbstractPDF (1060 KB)Oscillation Criteria for a Class of Fourth Order Differential EquationsKurt KreithSIAM Journal on Applied Mathematics, Vol. 22, No. 1 | 12 July 2006AbstractPDF (189 KB) Volume 17, Issue 5| 1969SIAM Journal on Applied Mathematics835-1015 History Submitted:05 January 1968Published online:12 July 2006 InformationCopyright © 1969 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0117086Article page range:pp. 984-991ISSN (print):0036-1399ISSN (online):1095-712XPublisher:Society for Industrial and Applied Mathematics