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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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LYAPUNOV-TYPE INEQUALITIES FOR LOCAL FRACTIONAL DIFFERENTIAL SYSTEMS
Fractals, 2020This paper deals with the problem of Lyapunov inequalities for local fractional differential equations with boundary conditions. By using analytical method, a novel Lyapunov-type inequalities for the local fractional differential equations is provided. A systematic design algorithm is developed for the construction of Lyapunov inequalities.
Qi, Yongfang +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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2013
Introduction The eigenvalue problems for quasilinear and nonlinear operators present many differences with the linear case, and a Lyapunov inequality for quasilinear resonant systems showed the existence of eigenvalue asymptotics driven by the coupling of the equations instead of the order of the equations.
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Introduction The eigenvalue problems for quasilinear and nonlinear operators present many differences with the linear case, and a Lyapunov inequality for quasilinear resonant systems showed the existence of eigenvalue asymptotics driven by the coupling of the equations instead of the order of the equations.
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On Lyapunov type inequalities for symmetric functions
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 2019The author used mainly the Popoviciu inequality and the Bellman inequality to derive and prove some new Lyapunov-type inequalities for symmetric functions. Furthermore, the results obtained in some special cases yield the Mitrinović, Bullen and Vasić inequality and the Marcus-Lopes inequality.
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Lyapunov-type Inequalities and Applications to PDE
2005This work is devoted to the study of resonant nonlinear boundary problems with Neumann boundary conditions. First, we consider the linear case doing a careful analysis which involves Lyapunov-type inequalities with the Lp— norms of the coefficient function.
A. Cañada, J.A. Montero, S. Villegas
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Lyapunov-Type Inequalities for Fractional Differential Equations
2021In this chapter, we give a survey of the most basic results on Lyapunov-type inequalities for fractional differential equations, and we sketch some recent developments related to this type of inequalities.
Ravi P. Agarwal +2 more
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A Note on Multivariate Lyapunov-Type Inequality
2014We transfer the recent obtained result of univariate Lyapunov-type inequality for third order differential equations to the multivariate setting of a shell via the polar method. Our result is better than the result of Anastassiou [Appl. Math. Letters, 24 (2011), 2167-2171] for third order partial differential equations.
AKTAŞ, Mustafa, ÇAKMAK, Devrim
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Lyapunov Type Integral Inequalities for Certain Differential Equations
gmj, 1997Abstract In the present paper we establish Lyapunov type integral inequalities related to the zeros of solutions of certain second-order differential equations by using elementary analysis. We also present some immediate applications of our results to study the asymptotic behavior of solutions of the corresponding differential equations.
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On a Lyapunov-type inequality and the zeros of a certain Mittag–Leffler function
Journal of Mathematical Analysis and Applications, 2014Rui A C Ferreira
exaly