Publication details

Nonoscillation criteria and energy functional for even-order half-linear two-term differential equations


DOŠLÝ Ondřej RŮŽIČKA Vojtěch

Year of publication 2016
Type Article in Periodical
Magazine / Source Electron. J. Diff. Equations
MU Faculty or unit

Faculty of Science

Field General mathematics
Keywords even-order half-linear differential equation; energy functional; nonoscillation; Wirtinger inequality
Description 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.
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