Generalised criteria on delay dependent stability of highly nonlinear hybrid stochastic systems

Our recent paper [2] is the first to establish delay dependent criteria for highly nonlinear hybrid stochastic differential delay equations (SDDEs) (by highly nonlinear we mean the coefficients of the SDDEs do not have to satisfy the linear growth condition). This is an important breakthrough in the stability study as all existing delay stability criteria before could only be applied to delay equations where their coefficients are either linear or nonlin- ear but bounded by linear functions (namely, satisfy the linear growth condition). In this continuation, we will point out one restrictive condition imposed in our earlier paper [2]. We will then develop our ideas and methods there in order to remove this restrictive condition so that our improved results cover a much wider class of hybrid SDDEs

Comparison and Uniqueness Results for the Periodic Boundary Value Problem for Linear First-Order Differential Equations Subject to a Functional Perturbation

This is a post-peer-review, pre-copyedit version of a chapter published in Area I. et al. (eds) Nonlinear Analysis and Boundary Value Problems. NABVP 2018. Springer Proceedings in Mathematics & Statistics, vol 292. Springer, Cham. The final authenticated version is available online at: https://doi.org/10.1007/978-3-030-26987-6_14We improve some comparison results for the periodic boundary value problem related to a first-order differential equation perturbed by a functional term. The comparison results presented cover many cases as differential equations with delay, differential equations with maxima and integro-differential equations. The interesting case of functional perturbation with piecewise constant arguments is also analyzed