Oscillation Properties of Higher-Order Sublinear Differential Equations

For higher-order sublinear nonautonomous ordinary differential equations, necessary and sufficient conditions for the existence of properties A and B are obtained. In particular, we prove that if n is even, a > 0, and the function p : [ a , +∞) → (−∞, 0] is Lebesgue integrable on each finite inte...

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Bibliographic Details
Published in:Differential equations 2018-12, Vol.54 (12), p.1545-1559
Main Authors: Kiguradze, I. T., Kiguradze, T. I.
Format: Article
Language:English
Subjects:
Analysis
Difference and Functional Equations
Differential equations
Mathematics
Mathematics and Statistics
Ordinary Differential Equations
Partial Differential Equations
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Summary:For higher-order sublinear nonautonomous ordinary differential equations, necessary and sufficient conditions for the existence of properties A and B are obtained. In particular, we prove that if n is even, a > 0, and the function p : [ a , +∞) → (−∞, 0] is Lebesgue integrable on each finite interval, then, for the oscillation property of all proper solutions of the differential equation u ( n ) = p ( t ) ln(1+| u |) sgn( u ), it is necessary and sufficient that ∫ >a + mathvariant="normal">∞ >p ( >t ) l n t d t = − ∞ .
ISSN:0012-2661
1608-3083
DOI:10.1134/S0012266118120029