Oscillatory properties of linear third-order differential equations.
نویسندگان
چکیده
منابع مشابه
Approximately $n$-order linear differential equations
We prove the generalized Hyers--Ulam stability of $n$-th order linear differential equation of the form $$y^{(n)}+p_{1}(x)y^{(n-1)}+ cdots+p_{n-1}(x)y^{prime}+p_{n}(x)y=f(x),$$ with condition that there exists a non--zero solution of corresponding homogeneous equation. Our main results extend and improve the corresponding results obtained by many authors.
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The second order linear differential equation (p(x)y′)′ + q(x)y = 0 , x ∈ (0, x0] is considered, where p, q ∈ C1(0, x0], p(x) > 0, q(x) > 0 for x ∈ (0, x0]. Sufficient conditions are established for every nontrivial solutions to be nonrectifiable oscillatory near x = 0 without the Hartman–Wintner condition.
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Nonoscillatory second order differential equations always admit “special”, principal solutions. For a certain type of oscillatory equation principal pairs of solutions were introduced by Á. Elbert, F. Neuman and J. Vosmanský, Diff. Int. Equations 5 (1992), 945–960. In this paper, the notion of principal pair is extended to a wider class of oscillatory equations. Also an interesting property of ...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1970
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1970-0264162-2