Browsing by Author "Trofimchuk, Sergei I."

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On periodic solutions and global dynamics in a periodic differential delay equation

[OWP-2014-08] Ivanov, Anatoli F.; Trofimchuk, Sergei I. (Mathematisches Forschungsinstitut Oberwolfach, 2014-05-13)

Several aspects of global dynamics and the existence of periodic solutions are studied for the scalar differential delay equation $x'(t) = a(t)f(x([t-K]))$ , where $f(x)$ is a continuous negative feedback function, $x \cdot ...
Slowly oscillating wave solutions of a single species reaction-diffusion equation with delay

[OWP-2007-12] Trofimchuk, Elena; Tkachenko, Victor; Trofimchuk, Sergei I. (Mathematisches Forschungsinstitut Oberwolfach, 2007-03-28)

We study positive bounded wave solutions $u(t, x) = \phi(\nu \cdot x+ct)$ , $\phi(-\infty)=0$ , of equation $u_t(t, x)=\delta u(t,x)−u(t,x) +g(u(t−h,x))$ , $x \in \mathbb{R}^m$ (*). It is supposed that Eq. (∗) has exactly two ...