Results 1 to 10 of about 28,941 (115)
Lyapunov-type Inequalities for Partial Differential Equations [PDF]
Journal of Functional Analysis, 2013 In this work we present a Lyapunov inequality for linear and quasilinear elliptic differential operators in $N-$dimensional domains $\Omega$. We also consider singular and degenerate elliptic problems with $A_p$ coefficients involving the $p-$Laplace ...
Juan P. Pinasco, Napoli, Pablo L. De
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Lyapunov-type inequalities for n-dimensional quasilinear systems
Electronic Journal of Differential Equations, 2013 In this article, inspired by the paper of Yang et al [12], we establish new versions of Lyapunov-type inequalities for a certain class of Dirichlet quasilinear systems.
Mustafa Fahri Aktas
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LYAPUNOV-TYPE INEQUALITY FOR EXTREMAL PUCCI’S EQUATIONS [PDF]
Journal of the Australian Mathematical Society, 2020 AbstractIn this article, we establish a Lyapunov-type inequality for the following extremal Pucci’s equation:$$\begin{eqnarray}\left\{\begin{array}{@{}ll@{}}{\mathcal{M}}_{\unicode[STIX]{x1D706},\unicode[STIX]{x1D6EC}}^{+}(D^{2}u)+b(x)|Du|+a(x)u=0 & \text{in}~\unicode[STIX]{x1D6FA},\\ u=0 & \text{on}~\unicode[STIX]{x2202}\unicode[STIX]{x1D6FA},\
J. TYAGI, R. B. VERMA
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Lyapunov-type inequality and solution for a fractional differential equation
Journal of Inequalities and Applications, 2020 In this paper, we consider the linear fractional differential equation By obtaining the Green’s function we derive the Lyapunov-type inequality for such a boundary value problem.
Dexiang Ma, Zifa Yang
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A Lyapunov-Type Inequality for Partial Differential Equation Involving the Mixed Caputo Derivative
Mathematics, 2020 In this work, we derive a Lyapunov-type inequality for a partial differential equation on a rectangular domain with the mixed Caputo derivative subject to Dirichlet-type boundary conditions.
Jie Wang, Shuqin Zhang
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Asymptotic controllability and optimal control [PDF]
, 2012 We consider a control problem where the state must reach asymptotically a target while paying an integral payoff with a non-negative Lagrangian. The dynamics is just continuous, and no assumptions are made on the zero level set of the Lagrangian. Through
Motta, Monica, Rampazzo, Franco
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Journal of Inequalities and Applications, 2019 A Lyapunov-type inequality is derived for a nonlinear fractional boundary value problem involving Caputo-type fractional derivative. The obtained inequality provides a necessary condition for the existence of nontrivial solutions to the considered ...
Mohamed Jleli, Bessem Samet, Yong Zhou
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On the Lyapunov Type Inequality
Russian Mathematics, 2020 The author's main result concernes an estimate on the zeros of the solutions to a linear equation of the type \[ x''+p(t)x'(t)+q(t)x=0. \] When \(p(t)\) is identically equal to zero, Lyapunov provided the following result: if \(x(t)\) is a solution such that \(x(a)=x(b)=0\) and \(x(t)\ne0\) for every \(t\in(a,b)\), then \[ \int_a^b|q(t)|\,dt\ge\frac{4}{
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A generalized Lyapunov inequality for a higher-order fractional boundary value problem
Journal of Inequalities and Applications, 2016 In the paper, we establish a Lyapunov inequality and two Lyapunov-type inequalities for a higher-order fractional boundary value problem with a controllable nonlinear term. Two applications are discussed.
Dexiang Ma
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Lyapunov-type inequalities for third order nonlinear equations
Differential Equations & Applications, 2022 We derive Lyapunov-type inequalities for general third order nonlinear equations involving multiple $ψ$-Laplacian operators of the form \begin{equation*} (ψ_{2}((ψ_{1}(u'))'))' + q(x)f(u) = 0, \end{equation*} where $ψ_{2}$ and $ψ_{1}$ are odd, increasing functions, $ψ_{2}$ is super-multiplicative, $ψ_{1}$ is sub-multiplicative, and $\frac{1}{ψ_{1}}$ is
Behrens, Brian, Dhar, Sougata
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