On the oscillation of fourth-order delay differential equations
Abstract In the paper, fourth-order delay differential equations of the form (r3(r2(r1y′)′)′)′(t)+q(t)y(τ(t))=0 $$ \bigl(r_{3} \bigl(r_{2} \bigl(r_{1}y' \bigr)' \bigr)' \bigr)'(t) + q(t) y \bigl( \tau (t) \bigr) = 0 $$ under the assumption ∫t0∞dtri(t)<∞,i=1,2,3, $$ \int _{t_{0...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2019-03-01
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| Series: | Advances in Difference Equations |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13662-019-2060-1 |
| Summary: | Abstract In the paper, fourth-order delay differential equations of the form (r3(r2(r1y′)′)′)′(t)+q(t)y(τ(t))=0 $$ \bigl(r_{3} \bigl(r_{2} \bigl(r_{1}y' \bigr)' \bigr)' \bigr)'(t) + q(t) y \bigl( \tau (t) \bigr) = 0 $$ under the assumption ∫t0∞dtri(t)<∞,i=1,2,3, $$ \int _{t_{0}}^{\infty }\frac{\mathrm {d}t}{r_{i}(t)} < \infty , \quad 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. |
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| ISSN: | 1687-1847 |