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Global Null Controllability of Linear Control Processes with Positive Lyapunov Exponents
Published in K. D. Elworthy, W. Norrie Evenitt, E. Bruce Lee, Differential equations, dynamical systems, and control science, 2017
Russell Johnson, Mahesh Nerurkar
More precisely, for each pair of integers n,k > 0, let M(n,k) be the set of real n×k matrices. Let Cn,k be the set of all uniformly bounded, uniformly continuous functions from R to M(n,k), equipped with the topology of uniform convergence on compact sets (compact-open topology).
Existence of asymptotically periodic solutions of partial functional differential equations with state-dependent delay
Published in Applicable Analysis, 2021
Filipe Andrade, Claudio Cuevas, Hernán R. Henríquez
In the theory of retarded functional differential equations with unbounded delay frequently we need additional properties of the space to obtain some results. Next we denote by the space of continuous functions from into X with compact support. It is clear from the axioms of phase space that . In this work we consider the following axiom [14]. If a uniformly bounded sequence in converges to a function ϕ in the compact-open topology, then ϕ belongs to and , as .
Asymptotic behavior of solutions of some stochastic integro-differential equations with infinite delay
Published in Applicable Analysis, 2021
If , a>0, , is continuous on and , then for every the following conditions hold: is in ;;, where H>0 is a constant, , K is continuous, M is locally bounded and H, K, M are independent of .For the function in (A), is a -valued continuous function on .The space is complete.If is a bounded sequence in given by functions with compact support and in the compact-open topology, then and as .