Controllability of impulsive second-order nonlinear systems with nonlocal conditions in Banach spaces

2015 ◽  
Vol 2 (3) ◽  
pp. 203-218 ◽  
Author(s):  
G. Arthi ◽  
K. Balachandran
Keyword(s):  
Nonlinear Systems ◽  
Banach Spaces ◽  
Nonlocal Conditions ◽  
Second Order

scholarly journals Existence of mild solutions of second-order neutral functional differential inclusions with nonlocal conditions in Banach spaces

2004 ◽  
Vol 2004 (22) ◽  
pp. 1133-1149
Author(s):  
S. Marshal Anthoni ◽  
J.-H. Kim ◽  
J. P. Dauer
Keyword(s):  
Banach Spaces ◽  
Mild Solutions ◽  
Nonlocal Conditions ◽  
Second Order ◽  
Linear Operators ◽  
Bounded Linear ◽  
Cosine Families ◽  
Functional Differential ◽  
Functional Differential Inclusions ◽  
Condensing Maps

We study the existence of mild solutions of the nonlinear second-order neutral functional differential and integrodifferential inclusions with nonlocal conditions in Banach spaces. The results are obtained by using the theory of strongly continuous cosine families of bounded linear operators and a fixed point theorem for condensing maps due to Martelli.

scholarly journals An Existence Result for Second-Order Impulsive Differential Equations with Nonlocal Conditions

2010 ◽  
Vol 2010 ◽  
pp. 1-9 ◽  
Author(s):  
Meili Li ◽  
Haiqiang Liu
Keyword(s):  
Differential Equations ◽  
Banach Spaces ◽  
Existence Result ◽  
Existence Of Solutions ◽  
Nonlocal Conditions ◽  
Impulsive Differential Equations ◽  
Second Order

The Leray-Schauder alternative is used to investigate the existence of solutions for second-order impulsive differential equations with nonlocal conditions in Banach spaces. The results improve some recent results.

scholarly journals Approximate controllability of second-order nonlocal impulsive partial functional integro-differential evolution systems in Banach spaces

Filomat ◽  
2019 ◽  
Vol 33 (18) ◽  
pp. 5887-5912 ◽  
Author(s):  
Mahalingam Nagaraj ◽  
Velusamy Kavitha ◽  
Dumitru Baleanu ◽  
Mani Arjunan
Keyword(s):  
Differential Evolution ◽  
Banach Spaces ◽  
Approximate Controllability ◽  
Evolution Equations ◽  
Mild Solutions ◽  
Nonlocal Conditions ◽  
Sufficient Conditions ◽  
Second Order ◽  
Nonlinear Alternative ◽  
Banach Contraction

This manuscript is involved with a class of second-order impulsive partial functional integro-differential evolution equations with nonlocal conditions in Banach spaces. Sufficient conditions ensuring the existence and approximate controllability of mild solutions are established. Theory of cosine family, Banach contraction principle and Leray-Schauder nonlinear alternative fixed point theorem are employed for achieving the required results. An example is analyzed to illustrate the effectiveness of the outcome.

scholarly journals Second Approximate Solution of Duffing Equation with Strong Nonlinearity by Homotopy Perturbation Method

1970 ◽  
Vol 30 ◽  
pp. 59-75
Author(s):  
M Alhaz Uddin ◽  
M Abdus Sattar
Keyword(s):  
Approximate Solution ◽  
Nonlinear Systems ◽  
Perturbation Method ◽  
Differential System ◽  
Homotopy Perturbation Method ◽  
Approximate Solutions ◽  
Second Order ◽  
Strong Nonlinearity ◽  
Analytical Technique ◽  
Homotopy Perturbation

 In this paper, the second order approximate solution of a general second order nonlinear ordinary differential system, modeling damped oscillatory process is considered. The new analytical technique based on the work of He’s homotopy perturbation method is developed to find the periodic solution of a second order ordinary nonlinear differential system with damping effects. Usually the second or higher order approximate solutions are able to give better results than the first order approximate solutions. The results show that the analytical approximate solutions obtained by homotopy perturbation method are uniformly valid on the whole solutions domain and they are suitable not only for strongly nonlinear systems, but also for weakly nonlinear systems. Another advantage of this new analytical technique is that it also works for strongly damped, weakly damped and undamped systems. Figures are provided to show the comparison between the analytical and the numerical solutions. Keywords: Homotopy perturbation method; damped oscillation; nonlinear equation; strong nonlinearity. GANIT J. Bangladesh Math. Soc. (ISSN 1606-3694) 30 (2010) 59-75  DOI: http://dx.doi.org/10.3329/ganit.v30i0.8504

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