Electron. J. Diff. Equ.,
Vol. 2016 (2016), No. 95, pp. 117.
Nonoscillation criteria and energy functional for evenorder
halflinear twoterm differential equations
Ondrej Dosly, Vojtech Ruzicka
Abstract:
We investigate oscillatory properties of evenorder halflinear 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 HilleNehari 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: Evenorder halflinear differential equation; energy functional;
nonoscillation, Wirtinger inequality.
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Ondrej Dosly
Department of Mathematics and Statistics
Masaryk University
Kotlarska 2, CZ611 37 Brno, Czech Republic
email: dosly@math.muni.cz


Vojtech Ruzicka
Department of Mathematics and Statistics
Masaryk University
Kotlarska 2, CZ611 37 Brno, Czech Republic
email: 211444@mail.muni.cz

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