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71.
Global asymptotic stability and boundedness of certain multi‐delay functional differential equations of third order
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In this paper, the authors give sufficient conditions for the boundedness and global asymptotic stability of solutions to certain nonlinear multi‐delay functional differential equations of the third order. The technique of proof involves defining an appropriate Lyapunov‐Krasovskii functional and applying LaSalle's invariance principle. An example is included to illustrate the results. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
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Arron JR Winslow MM Polleri A Chang CP Wu H Gao X Neilson JR Chen L Heit JJ Kim SK Yamasaki N Miyakawa T Francke U Graef IA Crabtree GR 《Nature》2006,441(7093):595-600
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77.
Uniqueness and parameter dependence of positive solutions to higher order boundary value problems with fractional $q$-derivatives
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John R. Graef Lingju Kong Qingkai Kong Min Wang 《Journal of Applied Analysis & Computation》2013,3(1):21-35
The authors study a class of nonlinear higher order boundary value problem with fractional $q$-erivativesand dependence on a positive parameter $\lm$.The existence, uniqueness, and dependence of positive solutions on $\lm$ are discussed.Two sequences are constructed so that they converge uniformly to the unique solution of the problems.Two examples are included in the paper. Numerical computations of the examples confirm their theoretical results. 相似文献
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Summary In addition to obtaining sufficient conditions for continuability of solutions of x″ + q(t)f(x)=r(t), some sufficient conditions
and some necessary and sufficient conditions for boundedness are obtained. The asymptotic behavior of solutions is studied
through examination of r(t)/q(t) as t → ∞.
Supported by Mississippi State University Biological and Physical Sciences Research Institute.
Entrata in Redazione il 6 febbraio 1973. 相似文献
79.
Explicit quadratic Liapunov functions that provide necessaryand sufficient conditions for the asymptotic stability of thesystem of linear difference equations x (t + 1) = Ax(t) areconstructed by transforming the original systems to y (t + 1)= Gy(t), where G is a companion matrix associated with the characteristicpolynomial of A. A necessary and sufficient condition for allroots of the characteristic polynomial to lie in the unit circle|z| < 1 on the complex plane is also derived. 2000 MathematicalsSubject Classification 39A11, 93D05. 相似文献
80.
In this paper, an nth order functional differential equation is considered for which the generalized Emden-Fowler-type equation
(0.1) 相似文献