The Operator Equation Ax — XD 2 = — δ 0 and Second Order Differential Equations in Banach Spaces

2000 ◽  
pp. 352-363
Author(s):  
Elena Schüler ◽  
Vu Quoc Phong
Keyword(s):  
Differential Equations ◽  
Banach Spaces ◽  
Operator Equation ◽  
Second Order ◽  
Second Order Differential Equations

On the growth of solutions to second order differential equations in Banach spaces

1985 ◽  
Vol 101 (3-4) ◽  
pp. 237-252 ◽  
Author(s):  
H. O. Fattorini
Keyword(s):  
Hilbert Space ◽  
Differential Equations ◽  
Banach Spaces ◽  
Complex Number ◽  
Exponential Growth ◽  
Second Order ◽  
Second Order Differential Equations ◽  
Arbitrary Complex Number ◽  
Arbitrary Complex ◽  
Growth Of Solutions

SynopsisWe obtain estimates for the exponential growth of the solutions to u″(t) = (A + ζ2I)u(t) in terms of the exponential growth of the solutions to u″(t) = Au(t), where ζ is an arbitrary complex number. Estimates in exponentially weighted L2 norms are also considered in Hilbert space.

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.

scholarly journals New oscillation criteria for second-order neutral differential equations with distributed deviating arguments

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Osama Moaaz ◽  
Choonkil Park ◽  
Elmetwally M. Elabbasy ◽  
Waed Muhsin
Keyword(s):  
Differential Equations ◽  
Second Order ◽  
The Other ◽  
Riccati Transformation ◽  
Transformation Technique ◽  
Deviating Arguments ◽  
Neutral Differential Equations ◽  
Second Order Differential Equations ◽  
Continuous Delay ◽  
New Criteria

AbstractIn this work, we create new oscillation conditions for solutions of second-order differential equations with continuous delay. The new criteria were created based on Riccati transformation technique and comparison principles. Furthermore, we obtain iterative criteria that can be applied even when the other criteria fail. The results obtained in this paper improve and extend the relevant previous results as illustrated by examples.

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