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Lyapunov-Type Inequalities for Difference Equations
2021In this chapter, we give a survey of the most basic results on Lyapunov-type inequalities for difference equations, discrete systems, and partial difference systems. We sketch some recent developments related to this type of inequalities.
Ravi P. Agarwal +2 more
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On the algebraic Lyapunov inequality
Pollack Periodica, 2015Considering the continuous algebraic Lyapunov inequality and equation PA + A*P<0 , PA + A*P=Q, the aim of this paper is to give an algebraic proof of the Lyapunov theorem through mathematical induction. Moreover by the presented algorithm all positive definite solutions of the Lyapunov equation are given in the case, if the right hand side is ...
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On the multivariate Lyapunov inequalities
Applied Mathematics and Computation, 2014zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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About Multivariate Lyapunov Inequalities
2015We transfer here basic univariate Lyapunov inequalities to the multivariate setting of a shell by using the polar method.
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Lyapunov Inequalities and their Applications
2000For nearly 50 years Lyapunov inequalities have been an important tool in the study of differential equations. In this survey, building on an excellent 1991 historical survey by Cheng, we sketch some new developments in the theory of Lyapunov inequalities and present some recent disconjugacy results relating to second and higher order differential ...
Richard C. Brown, Don B. Hinton
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On inequalities of Lyapunov type
Applied Mathematics and Computation, 2003We generalize the classical Lyapunov inequality for second-order linear differential equations to nonlinear differential equations of second order and then to higher order linear differential equations.
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Lyapunov-type inequality for quasilinear systems
Applied Mathematics and Computation, 2012zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Yang, Xiaojing +2 more
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Lyapunov-type Inequalities for Differential Equations
Mediterranean Journal of Mathematics, 2006Let us consider the linear boundary value problem (0.1) $$ u^{\prime\prime}(x) + a(x)u(x) = 0,\ x \in (0,L),\ u^{\prime}(0) = u^{\prime}(L) = 0, $$ where $$a \in \Lambda
Antonio Cañada +2 more
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Some Elementary Variations of the Lyapunov Inequality
SIAM Journal on Applied Mathematics, 1978A moment inequality derived by Petrov [1] is shown to follow from the classical Lyapunov inequality applied to a certain conditional distribution. A general conditional version of the Lyapunov inequality is presented. The performance of the Petrov inequality is compared with that of a related tighter inequality (also obtained by conditioning) in the ...
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Inertia theorems for operator Lyapunov inequalities
Systems & Control Letters, 2001zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Sasane, AJ, Curtain, RF
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