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    Lyapunov-type Inequalities for Partial Differential Equations

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    In this work we present a Lyapunov inequality for linear and quasilinear elliptic differential operators in N−N-dimensional domains Ω\Omega. We also consider singular and degenerate elliptic problems with ApA_p coefficients involving the p−p-Laplace operator with zero Dirichlet boundary condition. As an application of the inequalities obtained, we derive lower bounds for the first eigenvalue of the p−p-Laplacian, and compare them with the usual ones in the literature

    On Lyapunov-Krasovskii Functionals for Switched Nonlinear Systems with Delay

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    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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