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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 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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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 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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Lyapunov-Type Inequality for Fractional Sub-Laplacians
2021In the present paper, we prove the Lyapunov-type inequality for the fractional sub-Laplacian on the homogeneous Lie groups. We give some consequences of the obtained inequality. In addition, we also show the fractional \(L^{2}\)-Hardy inequality for the fractional sub-Laplacian on the half-space.
Aidyn Kassymov, Durvudkhan Suragan
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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 inequality for quasilinear systems
Applied Mathematics and Computation, 2010A Lyapunov-type inequality is derived for the quasilinear system \[ -\left(r_1(x)|u'(x)|^{p-2}u'(x)\right)'=f_1(x) |u(x)|^{\alpha-2}u(x)|v(x)|^{\beta}, \] \[ -\left(r_2(x)|v'(x)|^{q-2}v'(x)\right)'=f_2(x) |u(x)|^{\theta}|v(x)|^{\gamma-2}v(x), \] where both components of the solution \((u(x),v(x))\) have consecutive zeros at the points \(a,b\in\mathbb R\
Tiryaki, Aydin, ÇAKMAK, DEVRİM
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Lyapunov-Type Inequalities for Nonlinear Differential Systems
2021In this chapter, we give a survey of the most basic results on Lyapunov-type inequalities for second-order nonlinear systems of differential equations under some boundary conditions. We also sketch some recent developments related to this type of inequalities.
Ravi P. Agarwal +2 more
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