On Second Order Sufficient Conditions for Structured Nonlinear Programs in Infinite-Dimensional Function Spaces

2020 ◽  
pp. 83-107 ◽  
Author(s):  
J. C. Dunn
Keyword(s):  
Sufficient Conditions ◽  
Function Spaces ◽  
Second Order ◽  
Infinite Dimensional ◽  
Nonlinear Programs ◽  
Second Order Sufficient Conditions

APPROXIMATE CONTROLLABILITY OF SECOND-ORDER STOCHASTIC DIFFERENTIAL EQUATIONS WITH IMPULSIVE EFFECTS

2010 ◽  
Vol 24 (14) ◽  
pp. 1559-1572 ◽  
Author(s):  
RATHINASAMY SAKTHIVEL ◽  
YONG REN ◽  
N. I. MAHMUDOV
Keyword(s):  
Biological Sciences ◽  
Differential Equations ◽  
Approximate Controllability ◽  
Sufficient Conditions ◽  
Impulsive Differential Equations ◽  
Second Order ◽  
Impulsive Effects ◽  
Infinite Dimensional ◽  
Infinite Dimensional Dynamical Systems ◽  
Necessary And Sufficient

Many practical systems in physical and biological sciences have impulsive dynamical behaviors during the evolution process which can be modeled by impulsive differential equations. In this paper, the approximate controllability of nonlinear second-order stochastic infinite-dimensional dynamical systems with impulsive effects is considered. By using the Holder's inequality, stochastic analysis and fixed point strategy, a new set of necessary and sufficient conditions are formulated which guarantees the approximate controllability of the nonlinear second-order stochastic system. The results are obtained under the assumption that the associated linear system is approximately controllable.

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