Sturm-type comparison theorems for first- and second-order differential equations with delays of variable sign

1982 ◽  
Vol 34 (2) ◽  
pp. 129-133 ◽  
Author(s):  
Yu. I. Domshlak
Keyword(s):  
Differential Equations ◽  
Second Order ◽  
Comparison Theorems ◽  
Variable Sign ◽  
Second Order Differential Equations

scholarly journals Levin's comparison theorems for nonlinear second order differential equations

1996 ◽  
Vol 9 (6) ◽  
pp. 29-35 ◽  
Author(s):  
R.P. Agarwal ◽  
Wei-Cheng Lian ◽  
Cheh-Chih Yeh
Keyword(s):  
Differential Equations ◽  
Second Order ◽  
Comparison Theorems ◽  
Second Order Differential Equations

4.—Comparison Theorems for a Class of Second-order Non-linear Ordinary Differential Equations

1975 ◽  
Vol 73 ◽  
pp. 77-84
Author(s):  
Donald C. Benson
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Comparison Theorem ◽  
Linear Equations ◽  
Second Order ◽  
Comparison Theorems ◽  
Linear Ordinary Differential Equations ◽  
Second Order Differential Equations ◽  
Liénard Equations ◽  
Fowler Equation

SynopsisIntegral inequalities are used to obtain comparison theorems for a class of second-order differential equations which includes the Emden-Fowler equation, certain Liénard equations, and linear equations of the form d2y/dx2+f(x)y = 0. For these linear equations the results below imply Sturm's classical comparison theorem.

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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