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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
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8. Willett, D., Oscillation on finite or infinite intervals of second order linear differential equations, Can. Math. Bull. 14 (1971), 539–550.Google Scholar