Nonlinear oscillations of fourth order quasilinear ordinary differential equations

作者：Kamo K^*; Usami H

来源：Acta Mathematica Hungarica, 2011, 132(3): 207-222.

DOI：10.1007/s10474-011-0127-x

• asymptotic behavior
• differential equation
• higher order
• oscillation

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.

• 出版日期2011-8