1,120 research outputs found
Lyapunov-type inequality for a class of Dirichlet quasilinear systems involving the (p1,p2,…,pn)-Laplacian
AbstractWe state and prove a generalized Lyapunov-type inequality for one-dimensional Dirichlet quasilinear systems involving the (p1,p2,…,pn)-Laplacian. Our result generalize the Lyapunov-type inequality given in Napoli and Pinasco (2006) [12]
On Lyapunov-type inequality for a class of quasilinear systems
In this paper, we establish a new Lyapunov-type inequality for quasilinear systems. Our result in special case reduces to the result of Watanabe et al. [J. Inequal. Appl. 242(2012), 1-8]. As an application, we also obtain lower bounds for the eigenvalues of corresponding systems
Lyapunov-type Inequalities for Partial Differential Equations
In this work we present a Lyapunov inequality for linear and quasilinear
elliptic differential operators in dimensional domains . We also
consider singular and degenerate elliptic problems with coefficients
involving the Laplace operator with zero Dirichlet boundary condition.
As an application of the inequalities obtained, we derive lower bounds for
the first eigenvalue of the Laplacian, and compare them with the usual ones
in the literature
Boundary stabilization of quasilinear hyperbolic systems of balance laws: Exponential decay for small source terms
We investigate the long-time behavior of solutions of quasilinear hyperbolic
systems with transparent boundary conditions when small source terms are
incorporated in the system. Even if the finite-time stability of the system is
not preserved, it is shown here that an exponential convergence towards the
steady state still holds with a decay rate which is proportional to the
logarithm of the amplitude of the source term. The result is stated for a
system with dynamical boundary conditions in order to deal with initial data
that are free of any compatibility condition
Lyapunov-type inequalities for quasilinear systems with antiperiodic boundary conditions
We establish some new Lyapunov-type inequalities for one-dimensional p-Laplacian systems with antiperiodic boundary conditions. The lower bounds of eigenvalues are presented.Встановлено дєякі нові нєрівності типу Ляпунова для одновимірних p-лапласових систем з антиперіодичними граничними умовами. Наведено нижні межі для власних значень
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