*Correspondence: [email protected] College of Mathematics and Computer Science, Fuzhou University, Fuzhou, 350116, P.R. China Abstract Choosing space Cg as the phase space, the existence, uniqueness and stability of the solution to neutral stochastic functional differential equations with infinite delay (short for INSFDEs) are studied in this paper. Under non-Lipschitz condition, weakened ...

Numerous models of industrial processes such as diffusion in glassy polymers or solidification phenomena, lead to general one-phase free boundary value problems with phase onset. In this paper we develop a framework viable to prove global existence and stability of planar solutions to one such multidimensional model whose application is in controlled-release pharmaceuticals. We utilize a bounda...

In the present paper, we consider multidimensional nonlinear backward stochastic differential equations (BSDEs) with a driver depending on martingale part M of solution. We assume that term is merely monotone continuous respect to state variable. As regularity variable, very general condition which permits path-dependence “the future” process as well dependence its law (McKean–Vlasov-type equat...

The purpose of this paper is to present some coupled fixed point results on a metric space endowed with two $b$-metrics. We shall apply a fixed point theorem for an appropriate operator on the Cartesian product of the given spaces endowed with directed graphs. Data dependence, well-posedness and Ulam-Hyers stability are also studied. The results obtained here will be applied to prove the existe...

This paper deals with the system of functional-diierential equations dx(t) dt = p(x)(t) + q(t); where p : C!(R n) ! L!(R n) is a linear bounded operator, q 2 L!(R n), ! > 0 and C!(R n) and L!(R n) are spaces of n-dimensional !-periodic vector functions with continuous and integrable on 0;!] components, respectively. Conditions which guarantee the existence of a unique !-periodic solution and co...

We prove existence and uniqueness results in the presence of coupled lower and upper solutions for the general nth problem in time scales with linear dependence on the ith ∆derivatives for i= 1,2, . . . ,n, together with antiperiodic boundary value conditions. Here the nonlinear right-hand side of the equation is defined by a function f (t,x) which is rd-continuous in t and continuous in x unif...

A hybrid automaton is a model of a system with interacting continuous and discrete dynamics. It has been successfully employed in emerging applications on the border between computer science and control theory. In this paper, hybrid automata are formally introduced. Some results on existence and uniqueness of executions for hybrid automata are obtained. Continuous dependence on initial states a...

Semilinear stochastic evolution equations with multiplicative L'evy noise are considered‎. ‎The drift term is assumed to be monotone nonlinear and with linear growth‎. ‎Unlike other similar works‎, ‎we do not impose coercivity conditions on coefficients‎. ‎We establish the continuous dependence of the mild solution with respect to initial conditions and also on coefficients. ‎As corollaries of ...