scholarly journals The Dirichlet Problem for a Singular Singularly Perturbed Quasilinear Second Order Differential System

1997 ◽  
Vol 210 (1) ◽  
pp. 308-336 ◽  
Author(s):  
Huai-Ping Zhu
Keyword(s):  
Dirichlet Problem ◽  
Differential System ◽  
Second Order ◽  
Singularly Perturbed

An Asymptotical Stability in Variational Sense for Second Order Systems

2010 ◽  
Vol 10 (1) ◽  
Author(s):  
Dariusz Idczak ◽  
Stanisław Walczak
Keyword(s):  
Sobolev Space ◽  
Differential System ◽  
Sufficient Conditions ◽  
Zero Solution ◽  
Second Order ◽  
Functional Parameter ◽  
Asymptotical Stability ◽  
Parameter Control ◽  
Initial Condition ◽  
Second Order Systems

AbstractIn this paper, a new, variational concept of asymptotical stability of zero solution to an ordinary differential system of the second order, considered in Sobolev space, is presented. Sufficient conditions for an asymptotical stability in a variational sense with respect to initial condition and functional parameter (control) are given. Relation to the classical asymptotical stability is illustrated.

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