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8.—On Second-order Differential Inequalities

Published online by Cambridge University Press:  14 February 2012

F. V. Atkinson
F. V. Atkinson
Affiliation:
Department of Mathematics, University of Toronto.
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Synopsis

This paper is devoted to a study of differential equations and inequalities of the form

and

The results are mainly concerned with the existence of positive solutions, their uniqueness in the case of (*), and bounds for these solutions.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 72 , Issue 2 , 1974 , pp. 109 - 127
Copyright
Copyright © Royal Society of Edinburgh 1974

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References

References to Literature

[1]Atkinson, F. V., 1955.On second-order non-linear oscillations Pacif. J. Math., 5, 643–647.CrossRefGoogle Scholar
[2]Coffman, C. V. and Wong, J. S. W., 1970.On a second-order nonlinear oscillation problem. Trans. Am. Math. Soc., 147, 357–366.CrossRefGoogle Scholar
[3]Coffman, C. V. and Wong, J. S. W., 1972.Oscillation and nonoscillation of solutions of generalised Emden-Fowler equations. Trans. Am. Math. Soc., 167, 399–434.CrossRefGoogle Scholar
[4]Collatz, L., 1966. Functional Analysis and Numerical Mathematics. New York and London: Academic Press.Google Scholar
[5]Day, M. M., 1962. Normed linear spaces. Ergebn. Math., 21, (2nd edn.).CrossRefGoogle Scholar
[6]Grimmer, R. C., 1972.On non-oscillatory solutions of a nonlinear differential equation Proc. Am. Math. Soc., 34, 118–120.CrossRefGoogle Scholar
[7]Hammett, M. E., 1971.Nonoscillation properties of a nonlinear differential equation. Proc. Am. Math. Soc., 30, 92–96.CrossRefGoogle Scholar
[8]Heidel, J. W. and Hinton, D. B., 1972. Existence of oscillatory solutions for a nonlinear differential equation. Siamj. Math. Anal., 3, 344–351.CrossRefGoogle Scholar
[9]Kartsatos, A. G., 1972.Maintenance of oscillations under the effect of a periodic forcing term. Proc Am. Math. Soc., 33, 377–383.CrossRefGoogle Scholar
[10]Kurzweil, J., 1960.A note on oscillatory solutions of the equation Čas. Pěst. Mat., 85, 357–358.CrossRefGoogle Scholar
[11]Nehari, Z., 1960.On a class of nonlinear second-order differential equations. Trans. Am. Math. Soc., 95, 101–123.CrossRefGoogle Scholar
[12]Onose, H., 1972.On oscillations for solutions of nth order differential equations. Proc. Am. Math. Soc., 33, 495–500.Google Scholar
[13]TeufelH., Jr. H., Jr. 1972.Forced second-order non-linear oscillations. J Math. Anal. Applic., 40, 148–152.CrossRefGoogle Scholar
[14]TeufelH., Jr. H., Jr. 1972.A note on second-order differential equations and functional differential equations. Pacif. J. Math., 41, 537–541.CrossRefGoogle Scholar
[15]Wong, J. S. W., 1969.On second-order nonlinear oscillation. Funkcialaj Ekvacioj, 11, 207–234.Google Scholar
[16]Wong, J. S. W., 1969.Oscillation and nonoscillation of solutions of second-order linear differential equations with integrable coefficients. Trans. Am. Math. Soc., 144, 197–215.CrossRefGoogle Scholar