In this paper, two problems related to FitzHugh–Nagumo lattice systems are analyzed. The first one is concerned with the asymptotic behavior of random delayed driven by nonlinear Wong–Zakai noise. We obtain a new result ensuring that such system approximates corresponding deterministic when correlation time noise goes infinity rather than zero. prove existence tempered attractors for drift func...

We root this tribute to Nicholas Yannelis in Chapter II of his 1983 Rochester Ph.D. dissertation, and paper with Prabhakar: work strengthens the lower semicontinuity assumption Michael’s continuous selection theorem open sections, leads correspondences defined on a paracompact space values Hausdorff linear topological space. move beyond literature provide necessary sufficient condition for uppe...

We give a new proof of sequential weak* lower semicontinuity in BV(Ω;Rm) for integral functionals of the form F(u) := ∫

A general lower semicontinuity theorem, in which not only mappings uM and PM but also the integrands fM depend on M , is proved for integrands f, fM under certain general hypotheses including that f(x, u, P ) is convex respect to P and fM converge to f locally uniformly, but fM (x, u, P ) are not required to be convex respect to P and fM (x, ·, ·) do not even need to be lower semicontinuous. So...

This paper sets out a theoretical framework for approximating the attractor si of a semigroup S{t) defined on a Banach space A" by a q-step semidiscretization in time with constant steplength k . Using the one-step theory of Hale, Lin and Raugel, sufficient conditions are established for the existence of a family of attractors {$fk } c Xq , for the discrete semigroups S£ defined by the numerica...

of a Delay-Di erential Equation Tom a s Gedeon1 Department of Mathematical Sciences, Montana State University, Bozeman,MT 59717 [email protected] Gwendolen Hines2 Department of Mathematics and Statistics, University of Nebraska, Lincoln, NE 68588 [email protected] In this paper, we consider a discrete delay problem with negative feedback _ x(t) = f(x(t); x(t 1)) along with a ce...