On the -dichotomy for homogeneous linear differential equations.
We study positive linear Volterra integro-differential equations in Banach lattices. A characterization of positive equations is given. Furthermore, an explicit spectral criterion for uniformly asymptotic stability of positive equations is presented. Finally, we deal with problems of robust stability of positive systems under structured perturbations. Some explicit stability bounds with respect to these perturbations are given.
Generalizations of the theorem of Forelli to holomorphic mappings into complex spaces are given.
General nonlinear Volterra difference equations with infinite delay are considered. A new explicit criterion for global exponential stability is given. Furthermore, we present a stability bound for equations subject to nonlinear perturbations. Two examples are given to illustrate the results obtained.
We present new explicit criteria for exponential stability of general linear neutral time-varying differential systems. Particularly, our results give extensions of the well-known stability criteria reported in [3,11] to linear neutral time-varying differential systems with distributed delays.
Let be a tree. Then a vertex of with degree one is a leaf of and a vertex of degree at least three is a branch vertex of . The set of leaves of is denoted by and the set of branch vertices of is denoted by . For two distinct vertices , of , let denote the unique path in connecting and Let be a tree with . For each leaf of , let denote the nearest branch vertex to . We delete from for all . The resulting subtree of is called the reducible stem of and denoted...
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