On the oscillation of fourth-order delay differential equations

In the paper, fourth-order delay differential equations of the form ( r 3 ( r 2 ( r 1 y ′ ) ′ ) ′ ) ′ ( t ) + q ( t ) y ( τ ( t ) ) = 0 under the assumption ∫ t 0 ∞ d t r i ( t ) < ∞ , i = 1 , 2 , 3 , are investigated. Our newly proposed approach allows us to greatly reduce a number of conditions...

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Bibliographic Details
Published in:Advances in difference equations 2019-03, Vol.2019 (1), p.1-15, Article 118
Main Authors: Grace, Said R., Džurina, Jozef, Jadlovská, Irena, Li, Tongxing
Format: Article
Language:English
Subjects:
Analysis
Delay
Difference and Functional Equations
Differential equations
Fourth-order
Functional Analysis
Linear differential equation
Mathematical analysis
Mathematics
Mathematics and Statistics
Noncanonical operator
Ordinary Differential Equations
Oscillation
Partial Differential Equations
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Summary:In the paper, fourth-order delay differential equations of the form ( r 3 ( r 2 ( r 1 y ′ ) ′ ) ′ ) ′ ( t ) + q ( t ) y ( τ ( t ) ) = 0 under the assumption ∫ t 0 ∞ d t r i ( t ) < ∞ , i = 1 , 2 , 3 , are investigated. Our newly proposed approach allows us to greatly reduce a number of conditions ensuring that all solutions of the studied equation oscillate. An example is also presented to test the strength and applicability of the results obtained.
ISSN:1687-1847
1687-1839
1687-1847
DOI:10.1186/s13662-019-2060-1