Ondrej Dosly, Vojtech Ruzicka
Abstract:
We investigate oscillatory properties of even-order half-linear differential
equations and conditions for negativity of the associated energy functional.
First, using the relationship between positivity of the functional and
nonoscillation of the investigated equation, we prove Hille-Nehari type
nonoscillation criteria which extend criteria known in the linear case.
In the second part of the paper, we present conditions which guarantee
that the energy functional attains a negative value, i.e., it is unbounded
below.
Submitted July 27, 2015. Published April 12, 2016.
Math Subject Classifications: 34C10.
Key Words: Even-order half-linear differential equation; energy functional;
nonoscillation, Wirtinger inequality.
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Ondrej Dosly Department of Mathematics and Statistics Masaryk University Kotlarska 2, CZ-611 37 Brno, Czech Republic email: dosly@math.muni.cz |
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Vojtech Ruzicka Department of Mathematics and Statistics Masaryk University Kotlarska 2, CZ-611 37 Brno, Czech Republic email: 211444@mail.muni.cz |
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