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## Discussiones Mathematicae, Differential Inclusions, Control and Optimization

1998 | 18 | 1-2 | 5-17
Tytuł artykułu

### Positive coefficients case and oscillation

Autorzy
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We consider the second order self-adjoint differential equation
(1) (r(t)y'(t))' + p(t)y(t) = 0
on an interval I, where r, p are continuous functions and r is positive on I. The aim of this paper is to show one possibility to write equation (1) in the same form but with positive coefficients, say r₁, p₁ and to derive a sufficient condition for equation (1) to be oscillatory in the case p is nonnegative and $∫^∞ [1/r(t)]dt$ converges.
Słowa kluczowe
EN
Kategorie tematyczne
Rocznik
Tom
Numer
Strony
5-17
Opis fizyczny
Daty
wydano
1998
otrzymano
1998-04-06
Twórcy
autor
• Department of Mathematics, P.J. Šafarik University, 041-54 Košice, Slovakia
Bibliografia
• [1] J.H. Barrett, Oscillation theory of ordinary linear differential equations, Advances in Math. 3 (1969), 415-509.
• [2] M. Cecchi, M. Marini and G. Villari, Integral criteria for a classification of solutions of linear differential equations, J. Differential Equations 99 (1992), 381-397.
• [3] B.J. Harris On the oscillation of solutions of linear differential equations, Mathematika 31 (1984), 214-226.
• [4] Ch. Huang, Oscillation and nonoscillation for second order linear differential equations, J. Math. Anal. Appl. 210 (1997), 712-723.
• [5] W. Leighton, Principal quadratic functionals and self-adjoint second-order differential equations, Proc. Nat. Acad. Sci. 35 (1949), 192-193.
• [6] J. Ohriska, Oscillation of second order delay and ordinary differential equation, Czechoslovak Math. J. 34 (109) (1984), 107-112.
• [7] J. Ohriska, Oscillation of differential equations and v-derivatives, Czechoslovak Math. J. 39 (114) (1989), 24-44.
• [8] J. Ohriska, On the oscillation of a linear differential equation of second order, Czechoslovak Math. J. 39 (114) (1989), 16-23.
• [9] R. Oláh, Integral conditions of oscillation of a linear differential equation, Math. Slovaca 39 (1989), 323-329.
• [10] W.T. Reid, Sturmian theory for ordinary differential equations, Springer-Verlag New York Inc. (1980).
• [11] D. Willett, Classification of second order linear differential equations with respect to oscillation, Advances in Math. 3 (1969), 594-623.
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