Hostname: page-component-586b7cd67f-t7fkt Total loading time: 0 Render date: 2024-11-24T04:39:01.177Z Has data issue: false hasContentIssue false

Asymptotic Behaviour of Disconjugate nth Order Differential Equations

Published online by Cambridge University Press:  20 November 2018

D. Willett*
Affiliation:
University of Utah, Salt Lake City, Utah
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

An ordered set (u1, …, un) of positive Cn(a, b)-solutions of the linear differential equation

1.1

will be called fundamental principal system on [a, b) provided that

1.2

and

1.3

A system (u1, …, un) satisfying just (1.2) will be called a principal system on [a, b). In any principal system (u1, …, un) the solution u1 will be called a minimal solution.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1971

References

1. Dini, U., Studii sulle equazioni differenziali lineari, Ann. Mat. Pura Appl. (3) 11 (1905), 285335.Google Scholar
2. Dunkel, O., Regular singular points of a system of homogeneous linear differential equations of the first order, Amer. Acad. Arts and Sci. 88 (1902), 339370.Google Scholar
3. Faedo, S., II teorema di Fuchs per le equazioni differenziali lineari a coefficient non analitici e propriété asintotiche delle soluzioni, Ann. Mat. Pura Appl. (4) 25 (1946), 111133.Google Scholar
4. Faedo, S., Sulla stability delle soluzioni delle equazioni differenziali lineari. I, II, III, IV, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Nat. (8) 2 (1947), 564570, 757-764; 8 (1947), 37-43, 192-198.Google Scholar
5. Fink, A. M., An extension of Polya's theorem, J. Math. Anal. Appl. 28 (1968), 625627.Google Scholar
6. Ghizzetti, A., Sul comportamento asintotico degli integrali delle equazioni differenziali ordinarie, lineari ed omogenee, Giorn. Mat. Battaglini (4) 1 (77) (1947), 527.Google Scholar
7. Halanay, A., Comportement asymptotique des solutions des equations du second ordre dans le cas de la non-os dilation, Com. Acad. R. P. Romîne 9 (1959), 11211128. (Romanian)Google Scholar
8. Haie, J. K. and Onuchic, N., On the asymptotic behavior of solutions of a class of d.e.s., Contributions to Differential Equations 2 (1963), 6175 Google Scholar
9. Hartman, P., Principal solutions of disconjugate nth order linear differential equations, Amer. J. Math. 91 (1969), 306362.Google Scholar
10. Katz, I. N., Asymptotic behavior of solutions to some nth order linear differential equations, Proc. Amer. Math. Soc. 21 (1969), 657662.Google Scholar
11. Locke, P., On the asymptotic behavior of an nth order nonlinear equation, Proc. Amer. Math. Soc. 18 (1967), 383390.Google Scholar
12. Morse, M. and Leighton, W., Singular quadratic functional, Trans. Amer. Math. Soc. 40 (1936), 252286.Google Scholar
13. Pólya, G., On the mean-value theorem corresponding to a given linear homogeneous differential equation, Trans. Amer. Math. Soc. 24 (1922), 312324.Google Scholar
14. Ráb, M., Asymptotische Eigenschaften der Lösungen der Differentialgleichung y” + A(x)y = 0, Czech. Math. J. 83 (1958), 513519.Google Scholar
15. Sherman, T., Properties of solutions of nth order linear differential equations, Pacific J. Math. IS (1965), 10451060.Google Scholar
16. Sherman, T., On solutions of nth order linear differential equations with n zeros, Bull. Amer. Math. Soc. 74 (1968), 923925.Google Scholar
17. Trench, W. F., On the asymptotic behavior of solutions to second-order linear differential equations, Proc. Amer. Math. Soc. 14 (1963), 1214.Google Scholar
18. Waltman, P., On the asymptotic behavior of solutions of an nth order equation, Monatsh. Math. 69 (1965), 427430.Google Scholar
19. Waltman, P., Qn the asymptotic behavior of a nonlinear equation, Proc. Amer. Math. Soc. 15 (1964), 918923.Google Scholar
20. Zlámal, M., Asymptotische Eigenschaften der Lösungen linearer Differentialgleichungen, Math. Nachr. 10 (1953), 169174.Google Scholar