scholarly journals Asymptotic Stability of Neutral Set-Valued Functional Differential Equation by Fixed Point Method

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Junyan Bao ◽  
Peiguang Wang
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Asymptotic Stability ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Fixed Point Method ◽  
Stability Theorem ◽  
Point Method ◽  
Functional Differential ◽  
Necessary And Sufficient

This paper studies a class of nonlinear neutral set-valued functional differential equations. The globally asymptotic stability theorem with necessary and sufficient conditions is obtained via the fixed point method. Meanwhile, we give an example to illustrate the obtained result.

A star-shaped condition for stability of linear retarded functional differential equations†

1979 ◽  
Vol 83 (3-4) ◽  
pp. 189-198 ◽  
Author(s):  
Richard Silkowski
Keyword(s):  
Asymptotic Stability ◽  
Linear Functional ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Retarded Functional Differential Equations ◽  
Region Of Stability ◽  
Linear Functional Differential Equation ◽  
Functional Differential ◽  
Image Position ◽  
Necessary And Sufficient

SYNOPSISSufficient conditions are developed for asymptotic stability of the autonomous linear functional differential equation of retarded type. If the asymptotic stability ofimplies the asymptotic stability ofthen these conditions are also necessary. Necessary and sufficient conditions are developed for the largest cone in the region of stability. These results are illustrated with the example

scholarly journals On periodic solutions to autonomous retarded functional differential equations

1990 ◽  
Vol 41 (3) ◽  
pp. 347-354
Author(s):  
Zhanyuan Hou
Keyword(s):  
Differential Equation ◽  
Periodic Solution ◽  
Periodic Solutions ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Sufficient Condition ◽  
Retarded Functional Differential Equations ◽  
Retarded Functional Differential Equation ◽  
Functional Differential ◽  
Necessary And Sufficient

Under the assumption that Ca = C([−r, 0], Sn−1(a)) is positively invariant for a > 0, two necessary and sufficient conditions are obtained for an autonomous retarded functional differential equation to have a non-trivial periodic solution in Ca. Moreover, a feasible sufficient condition is given, which is better for n = 2 than that given by Dos Reis and Baroni.

scholarly journals Fixed points and stability in nonlinear neutral integro-differential equations with variable delay

Filomat ◽  
2014 ◽  
Vol 28 (4) ◽  
pp. 781-795
Author(s):  
Imene Soualhia ◽  
Abdelouaheb Ardjouni ◽  
Ahcene Djoudi
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Initial Function ◽  
Unique Fixed Point ◽  
Complete Metric Space ◽  
Sufficient Conditions ◽  
Zero Solution ◽  
Stability Theorem ◽  
Variable Delay ◽  
Necessary And Sufficient

The nonlinear neutral integro-differential equation x'(t) = -?t,t-?(t) a (t,s) g(x(s))ds+c(t)x'(t-?(t)), with variable delay ?(t) ? 0 is investigated. We find suitable conditions for ?, a, c and g so that for a given continuous initial function ? mapping P for the above equation can be defined on a carefully chosen complete metric space S0? in which P possesses a unique fixed point. The final result is an asymptotic stability theorem for the zero solution with a necessary and sufficient conditions. The obtained theorem improves and generalizes previous results due to Burton [6], Becker and Burton [5] and Jin and Luo [16].

scholarly journals Fixed Points and Stability of a Class of Integrodifferential Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
Dingheng Pi
Keyword(s):  
Fixed Point ◽  
Fixed Point Theory ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Zero Solution ◽  
Point Theory ◽  
Asymptotically Stable ◽  
Variable Delay ◽  
Functional Differential ◽  
Necessary And Sufficient

We study a class of integrodifferential functional differential equationsx¨+f(t,x,x˙)x˙+∑j=1N∫t-rj(t)taj(t,s)gj(s,x(s))ds=0with variable delay. By using the fixed point theory, we establish necessary and sufficient conditions ensuring that the zero solution of this equation is asymptotically stable.

Asymptotic Behavior for Nonoscillatory Solutions of Second Order Nonlinear Functional Differential Equation

2012 ◽  
Vol 616-618 ◽  
pp. 2137-2141
Author(s):  
Zhi Min Luo ◽  
Bei Fei Chen
Keyword(s):  
Differential Equation ◽  
Asymptotic Behavior ◽  
Differential Equations ◽  
Functional Differential Equation ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Nonoscillatory Solutions ◽  
Nonlinear Functional ◽  
Nonlinear Functional Differential Equation ◽  
Functional Differential

This paper studied the asymptotic behavior of a class of nonlinear functional differential equations by using the Bellman-Bihari inequality. We obtain results which extend and complement those in references. The results indicate that all non-oscillatory continuable solutions of equation are asymptotic to at+b as under some sufficient conditions, where a,b are real constants. An example is provided to illustrate the application of the results.

scholarly journals On the positive solutions of a higher order functional differential equation with a discontinuity

1982 ◽  
Vol 5 (2) ◽  
pp. 263-273 ◽  
Author(s):  
John R. Graef ◽  
Paul W. Spikes ◽  
Myron K. Grammatikopoulos
Keyword(s):  
Differential Equation ◽  
Functional Differential Equation ◽  
Bounded Solution ◽  
Sufficient Conditions ◽  
Asymptotic Behavior Of Solutions ◽  
Bounded Solutions ◽  
Nonlinear Functional ◽  
Functional Differential ◽  
Necessary And Sufficient ◽  
Special Case

Then-th order nonlinear functional differential equation[r(t)x(n−υ)(t)](υ)=f(t,x(g(t)))is considered; necessary and sufficient conditions are given for this equation to have: (i) a positive bounded solutionx(t)→B>0ast→∞; and (ii) all positive bounded solutions converging to0ast→∞. Other results on the asymptotic behavior of solutions are also given. The conditions imposed are such that the equation with a discontinuity[r(t)x(n−υ)(t)](υ)=q(t)x−λ,   λ>0is included as a special case.

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