Leighton, Walter; Nehari, Zeev On the oscillation of solutions of self-adjoint linear differential equations of the fourth order. (English) Zbl 0084.08104 Trans. Am. Math. Soc. 89, 325-377 (1959). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 1 ReviewCited in 110 Documents Keywords:ordinary differential equations PDF BibTeX XML Cite \textit{W. Leighton} and \textit{Z. Nehari}, Trans. Am. Math. Soc. 89, 325--377 (1959; Zbl 0084.08104) Full Text: DOI References: [1] George D. Birkhoff, On the solutions of ordinary linear homogeneous differential equations of the third order, Ann. of Math. (2) 12 (1911), no. 3, 103 – 127. · JFM 42.0344.01 [2] Gianfranco Cimmino, Autosoluzioni e autovalori nelle equazioni differenziali lineari ordinarie autoaggiunte di ordine superiore, Math. Z. 32 (1930), no. 1, 4 – 58 (Italian). · JFM 56.0397.01 [3] R. Courant and D. Hilbert, Methods of mathematical physics. Vol. I, Interscience Publishers, Inc., New York, N.Y., 1953. · Zbl 0051.28802 [4] William Benjamin Fite, Concerning the zeros of the solutions of certain differential equations, Trans. Amer. Math. Soc. 19 (1918), no. 4, 341 – 352. [5] Einar Hille, Non-oscillation theorems, Trans. Amer. Math. Soc. 64 (1948), 234 – 252. · Zbl 0031.35402 [6] E. Kamke, Differentialgleichungen, Lösungsmethoden und Lösungen, 3 Aufl., New York, Chelsea. · Zbl 0026.31801 [7] Walter Leighton, On self-adjoint differential equations of second order, J. London Math. Soc. 27 (1952), 37 – 47. · Zbl 0048.06503 [8] Richard A. Moore, The behavior of solutions of a linear differential equation of second order, Pacific J. Math. 5 (1955), 125 – 145. · Zbl 0064.08401 [9] Marston Morse, The calculus of variations in the large, American Mathematical Society Colloquium Publications, vol. 18, American Mathematical Society, Providence, RI, 1996. Reprint of the 1932 original. · Zbl 0011.02802 [10] Zeev Nehari, Oscillation criteria for second-order linear differential equations, Trans. Amer. Math. Soc. 85 (1957), 428 – 445. · Zbl 0078.07602 [11] Clarence N. Reynolds Jr., On the zeros of solutions of homogeneous linear differential equations, Trans. Amer. Math. Soc. 22 (1921), no. 2, 220 – 229. · JFM 48.0525.02 [12] Marko Švec, Sur les dispersions des intégrales de l’équation \?\?\(^{4}\)\?+\?(\?)\?=0, Czechoslovak Math. J. 5(80) (1955), 29 – 60 (French, with Russian summary). · Zbl 0066.33405 [13] Wolfgan Sternberg, Die Entwicklung unstetiger Funktionen nach den Eigenfunktionen eines eindimensionalen Randwertproblems, Math. Z. 3 (1919), no. 1, 191 – 208 (German). · JFM 47.0419.02 [14] William M. Whyburn, On Self-Adjoint Ordinary Differential Equations of the Fourth Order, Amer. J. Math. 52 (1930), no. 1, 171 – 196. · JFM 56.0399.01 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.