scholarly journals Relative controllability of nonlinear neutral Volterra integrodifferential systems

1996 ◽  
Vol 37 (3) ◽  
pp. 346-353 ◽  
Author(s):  
K. Balachandran ◽  
J. P. Dauer
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Sufficient Conditions ◽  
Distributed Delays ◽  
Schauder’S Fixed Point Theorem ◽  
Control Variables ◽  
Relative Controllability ◽  
Schauder's Fixed Point Theorem

AbstractSufficient conditions are derived for the relative controllability of nonlinear neutral Volterra integrodifferential systems with distributed delays in the control variables. The results are a generalization of previous results and are obtained by using Schauder's fixed-point theorem.

Controllability of nonlinear perturbations of linear systems with distributed delays in control

Robotica ◽  
1985 ◽  
Vol 3 (2) ◽  
pp. 89-91 ◽  
Author(s):  
K. Balachandran
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Linear Systems ◽  
Point Theorem ◽  
Control Variable ◽  
Sufficient Conditions ◽  
Distributed Delays ◽  
Schauder’S Fixed Point Theorem ◽  
Nonlinear Perturbations ◽  
Relative Controllability

SUMMARYSufficient conditions are derived for the relative controllability of nonlinear perturbations of linear systems with distributed delays in control variable. The results are a generalization of previous results and are obtained by using Schauder's fixed point theorem.

scholarly journals Schauder’s fixed-point theorem in approximate controllability problems

2016 ◽  
Vol 26 (2) ◽  
pp. 263-275 ◽  
Author(s):  
Artur Babiarz ◽  
Jerzy Klamka ◽  
Michał Niezabitowski
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Dynamic Systems ◽  
Approximate Controllability ◽  
Nonlocal Conditions ◽  
Sufficient Conditions ◽  
Schauder’S Fixed Point Theorem ◽  
Differential Systems ◽  
Schauder's Fixed Point Theorem

AbstractThe main objective of this article is to present the state of the art concerning approximate controllability of dynamic systems in infinite-dimensional spaces. The presented investigation focuses on obtaining sufficient conditions for approximate controllability of various types of dynamic systems using Schauder’s fixed-point theorem. We describe the results of approximate controllability for nonlinear impulsive neutral fuzzy stochastic differential equations with nonlocal conditions, impulsive neutral functional evolution integro-differential systems, stochastic impulsive systems with control-dependent coefficients, nonlinear impulsive differential systems, and evolution systems with nonlocal conditions and semilinear evolution equation.

scholarly journals On the controllability of fractional dynamical systems

2012 ◽  
Vol 22 (3) ◽  
pp. 523-531 ◽  
Author(s):  
Krishnan Balachandran ◽  
Jayakumar Kokila
Keyword(s):  
Fixed Point ◽  
Dynamical Systems ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Matrix Function ◽  
Sufficient Conditions ◽  
Schauder’S Fixed Point Theorem ◽  
Finite Dimensional ◽  
Linear And Nonlinear ◽  
Controllability Grammian

Abstract This paper is concerned with the controllability of linear and nonlinear fractional dynamical systems in finite dimensional spaces. Sufficient conditions for controllability are obtained using Schauder’s fixed point theorem and the controllability Grammian matrix which is defined by the Mittag-Leffler matrix function. Examples are given to illustrate the effectiveness of the theory.

scholarly journals A Periodic Solution of the Generalized Forced Liénard Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Zahra Goodarzi ◽  
Abdolrahman Razani
Keyword(s):  
Periodic Solution ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Liénard Equation ◽  
Schauder’S Fixed Point Theorem ◽  
Schauder's Fixed Point Theorem ◽  
Lienard Equation

We consider the generalized forced Liénard equation as follows:(ϕp(x′))′+(f(x)+k(x)x′)x′+g(x)=p(t)+s. By applying Schauder's fixed point theorem, the existence of at least one periodic solution of this equation is proved.

scholarly journals Positive Solutions of a Singular Nonlocal Fractional Order Differential System via Schauder’s Fixed Point Theorem

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Xinguang Zhang ◽  
Cuiling Mao ◽  
Yonghong Wu ◽  
Hua Su
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Positive Solutions ◽  
Fractional Order ◽  
Differential System ◽  
Point Theorem ◽  
Schauder’S Fixed Point Theorem ◽  
Schauder's Fixed Point Theorem ◽  
Existence Of Positive Solutions ◽  
Two Parameters

We establish the existence of positive solutions to a class of singular nonlocal fractional order differential system depending on two parameters. Our methods are based on Schauder’s fixed point theorem.

Sign in / Sign up

Export Citation Format

Share Document