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A Generalization of Čaplygin's Inequality with Applications to Singular Boundary Value Problems

Published online by Cambridge University Press:  20 November 2018

D. Willett
D. Willett*
Affiliation:
University of Alberta, Edmonton, Alberta
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Let

(1.1)

where pk ∈ C(α, β) and - ∞ ≦ α < β ≦ ∞ . A solution of (1.1) is a nontrivial function y ∈ Cn(α, β), a neighborhood of β is an interval of the form (γ, β), α ≦ γ < β, and a neighborhood of α is an interval of the form (α, γ), α < γ ≦ β.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 25 , Issue 5 , October 1973 , pp. 1024 - 1039
Copyright
Copyright © Canadian Mathematical Society 1973

References

1. Bebernes, J. W. and Jackson, L. K., Infinite boundary value problems for y” = f(x, y), Duke Math. J. 34 (1967), 39–48.Google Scholar
2. Čaplygin, S. A., New methods in the approximate integration of differential equations (Russian), Moscow: Gosudarstv. Izdat. Tech.-Teoret. Lit. (1950).Google Scholar
3. Levin, A. Ju., Non-oscillation of solutions of the equation x(n) + p1(t)x(n_1) + … + pn(t)x = 0, Uspehi Mat. Nauk 24 (1969), 43-96. (Russian Math. Surveys 24 (1969), 43–100).Google Scholar
4. Pólya, G., On the mean-value theorem corresponding to a given linear homogeneous differential equation, Trans. Amer. Math. Soc. 24 (1922), 312–324.Google Scholar
5. Pólya, G. and Szegö, G., Aufgaben und Lehrsätze der Analysis, Vol. II (Springer-Verlag, Berlin, 1954).Google Scholar
6. Willett, D., Asymptotic behaviour of disconjugate nth. order differential equations, Can. J. Math. 23 (1971), 293–314.Google Scholar
7. Willett, D., Disconjugacy tests for singular linear differential equations, SI AM J. Math. Anal. 2 (1971), 536–545 (Errata : ibid, 3 (1972)).Google Scholar
8. Willett, D., Oscillation on finite or infinite intervals of second order linear differential equations, Can. Math. Bull. 14 (1971), 539–550.Google Scholar