Variational technique and principal solution in half-linear oscillation criteria

We investigate oscillatory properties of half-linear differential equations. The investigated half-linear equation is viewed as a perturbation of another (nonoscillatory) equation of the same form and perturbation is allowed both in the absolute term and in the derivative term. First, the Sturmian t...

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Bibliographic Details
Published in:Applied mathematics and computation 2011-02, Vol.217 (12), p.5385-5391
Main Authors: DOSLY, Ondřej, FISNAROVA, Simona
Format: Article
Language:English
Subjects:
Criteria
Derivatives
Differential equations
Exact sciences and technology
Half-linear differential equation
Linearization method
Mathematical analysis
Mathematical models
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Numerical methods in mathematical programming, optimization and calculus of variations
Numerical methods in optimization and calculus of variations
Ordinary differential equations
Oscillation and nonoscillation criteria
Oscillations
Perturbation methods
Perturbation principle
Riccati equation
Sciences and techniques of general use
Variational technique
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Summary:We investigate oscillatory properties of half-linear differential equations. The investigated half-linear equation is viewed as a perturbation of another (nonoscillatory) equation of the same form and perturbation is allowed both in the absolute term and in the derivative term. First, the Sturmian type theorem for solutions of the associated Riccati equation is established. In the second part of the paper we prove new half-linear oscillation criteria using the variational technique.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2010.12.006