Properties of Third-Order Nonlinear Functional Differential Equations with Mixed Arguments
The aim of this paper is to offer sufficient conditions for property (B) and/or the oscillation of the third-order nonlinear functional differential equation with mixed arguments [𝑎(𝑡)[𝑥″(𝑡)]𝛾]′=𝑞(𝑡)𝑓(𝑥[𝜏(𝑡)])+𝑝(𝑡)ℎ(𝑥[𝜎(𝑡)]). Both cases ∫∞𝑎−1/𝛾(𝑠)d𝑠=∞ and ∫∞𝑎−1/𝛾(𝑠)d𝑠<∞ are considered. We deduce...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2011-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2011/857860 |
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| Summary: | The aim of this paper is to offer sufficient conditions for property
(B) and/or the oscillation of the third-order nonlinear functional differential
equation with mixed arguments [𝑎(𝑡)[𝑥″(𝑡)]𝛾]′=𝑞(𝑡)𝑓(𝑥[𝜏(𝑡)])+𝑝(𝑡)ℎ(𝑥[𝜎(𝑡)]). Both cases ∫∞𝑎−1/𝛾(𝑠)d𝑠=∞ and ∫∞𝑎−1/𝛾(𝑠)d𝑠<∞ are considered. We
deduce properties of the studied equations via new comparison theorems. The
results obtained essentially improve and complement earlier ones. |
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| ISSN: | 1085-3375 1687-0409 |