5,433 research outputs found
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
On Lyapunov-Krasovskii Functionals for Switched Nonlinear Systems with Delay
We present a set of results concerning the existence of Lyapunov-Krasovskii
functionals for classes of nonlinear switched systems with time-delay. In
particular, we first present a result for positive systems that relaxes
conditions recently described in \cite{SunWang} for the existence of L-K
functionals. We also provide related conditions for positive coupled
differential-difference positive systems and for systems of neutral type that
are not necessarily positive. Finally, corresponding results for discrete-time
systems are described.Comment: 19 Page
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