Nonlinear oscillation of second order differential equations with retarded argument

1975 ◽  
Vol 106 (1) ◽  
pp. 171-185 ◽  
Author(s):  
Takaŝi Kusano ◽  
Manabu Naito
Keyword(s):  
Differential Equations ◽  
Nonlinear Oscillation ◽  
Second Order ◽  
Retarded Argument ◽  
Second Order Differential Equations

scholarly journals Linearization and Higher Order Nonlinear Oscillation Theorems Using Comparison Methods

2004 ◽  
Vol 11 (1) ◽  
pp. 7-26
Author(s):  
Ravi P. Agarwal ◽  
Said R. Grace ◽  
Donal O'Regan
Keyword(s):  
Differential Equations ◽  
Nonlinear Oscillation ◽  
Nonlinear Differential Equations ◽  
Main Idea ◽  
Higher Order ◽  
Second Order ◽  
Oscillation Criteria ◽  
Second Order Differential Equations ◽  
Comparison Methods ◽  
Oscillation Theorems

Abstract We establish some new oscillation criteria for higher order nonlinear differential equations. The main idea involves comparing our equation with the related linear second order differential equations so that the known oscillation theorems from the literature can be employed directly.

Banach Lie Algebroids

2011 ◽  
Vol 57 (2) ◽  
pp. 409-416
Author(s):  
Mihai Anastasiei
Keyword(s):  
Differential Equations ◽  
Smooth Manifold ◽  
Vector Bundles ◽  
Second Order ◽  
Lie Algebroids ◽  
Second Order Differential Equations

Banach Lie AlgebroidsFirst, we extend the notion of second order differential equations (SODE) on a smooth manifold to anchored Banach vector bundles. Then we define the Banach Lie algebroids as Lie algebroids structures modeled on anchored Banach vector bundles and prove that they form a category.

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