Abstract
A theorem of H. Weyl is extended by the establishment of bound estimates on some of the solutions of the second-order Duffing-type differential equation y″(x) + p(x)y′(x) = q(x) [y(x)]2k+1, where x ∈ J = {x: 0 ≤ x < ω ≤ ∞}, k = 0,1,2,..., and both p(x) and q(x) are continuous functions of x on J (with q(x) > 0).
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References
R. R. Burnside, A Nonoscillat ion Result. SIAM Review 23 (1981), 257–258.
W. J. Cunningham, Introduction to Nonlinear Analysis. McGraw-Hill Book Company, New York, 1958.
Philip Hartman, Ordinary Differential Equations. John Wiley and Sons, New York, 1964.
A. Kneser, Untersuchung und asymptotische Darstellung der Integrale gewisser Differentialgleichungen bei grossen reellen Werthen des Arguments. J. Reine Angew. Math. 116 (1896), 178–212 (X16, X115).
M. Picone and C. Miranda, Esercizi di Analisi Matematica. Studium Urbis, Rome, 1945.
O. Plaat, Ordinary Differential Equations. Holden-Day, San Francisco, 1971.
D. K. Ross, A nonoscillation result. SIAM Review 22 (1980), 229.
C. A. Swanson, Comparison and Oscillation Theory of Linear Differential Equations. Academic Press, New York, 1968.
Francesco Giacomo Tricomi, Differential Equations (English Translation). Blackie and Son, Glasgow, 1961.
H. Weyl, Ueber gewöhnliche lineare Differentialgleichungen mit singularën Stellen und ihre Eigenfunktionen. Nachrichten von der Königlichen Gesellschaft der Wissenschafben zu Göttingen (1909), 37-63.
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© 1983 Springer Basel AG
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Ross, D.K., Wallace, R.J. (1983). Bound Estimates on Solutions of a Second-Order Differential Equation of Duffing Type. In: Beckenbach, E.F., Walter, W. (eds) General Inequalities 3. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série internationale d’Analyse numérique, vol 64. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-6290-5_34
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DOI: https://doi.org/10.1007/978-3-0348-6290-5_34
Publisher Name: Birkhäuser, Basel
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