Perturbations of the half-linear Euler–Weber type differential equation
- 作者：Ondř ; ej Doš ; lý
- 关键词：Half-linear differential equation ; Euler– ; Weber equation ; Variational principle ; Riccati equation ; Principal solution
- 刊名：Journal of Mathematical Analysis and Applications
- 出版年：2006
- 期刊代码：76_0022247x
- 类别：mt
- 出版时间：1 November 2006
- 卷：323
- 期：1
- 页码：426-440
- 文件大小：156 K
摘要
We investigate oscillatory properties of the half-linear second order differential equation
viewed as a perturbation of another half-linear differential equation of the same form
The obtained oscillation and nonoscillation criteria are formulated in terms of the integral , where h is a function which is close to the principal solution of (*), in a certain sense. A typical model of (*) in applications is the half-linear Euler–Weber differential equation with the critical coefficients
we establish oscillation and nonoscillation criteria for perturbations of this equation. Some open problems and perspectives of the further research along this line are also formulated.