Nonlinear oscillations of fourth order quasilinear ordinary differential equations

We consider fourth order quasilinear ordinary differential equations. Firstly, we classify positive solutions into four types according to their asymptotic properties. Then we derive existence theorems of positive solutions belonging to each type. Using these results, we can obtain an oscillation cr...

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Bibliographic Details
Published in:Acta mathematica Hungarica Vol. 132; no. 3; pp. 207 - 222
Main Authors: Kamo, Ken-ichi, Usami, Hiroyuki
Format: Journal Article
Language:English
Published: Dordrecht Springer Netherlands 01.08.2011
Subjects:
Mathematics
Mathematics and Statistics
oscillation
differential equation
asymptotic behavior
higher order
34E05
34D05
ISSN:0236-5294, 1588-2632
Online Access:Get full text
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Summary:We consider fourth order quasilinear ordinary differential equations. Firstly, we classify positive solutions into four types according to their asymptotic properties. Then we derive existence theorems of positive solutions belonging to each type. Using these results, we can obtain an oscillation criterion, which is our main objective. Moreover, applying such criteria for ordinary differential equations to binary elliptic systems, we establish nonexistence theorems for positive solutions.
ISSN:0236-5294
1588-2632
DOI:10.1007/s10474-011-0127-x