This paper considers the Lurye system of a discrete-time, linear time-invariant plant in negative feedback with nonlinearity. Both monotone and slope-restricted nonlinearities are considered. The main result is procedure to construct destabilizing for system. If satisfies certain phase condition then nonlinearity can be constructed so that has non-trivial periodic cycle. Several examples provid...

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 ...

This paper is devoted to the solvability of an initial-boundary value problem for second-order parabolic equations in divergence form with variable order nonlinearity. The characteristic feature considered class Cauchy-Neumann fact that exponent p(t, x) and anisotropic diffusion tensor D(t, are not well predefined a priori, but instead these depend on solution this problem, i.e., p = x, u) D u)...

Abstract We prove a-posteriori error-estimates for reduced-order modeling of quasilinear parabolic PDEs with non-monotone nonlinearity. consider the solution a semi-discrete in space equation as reference, and therefore incorporate reduced basis-, empirical interpolation-, time-discretization-errors our consideration. Numerical experiments illustrate results.

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 corollarie...

we introduce a new concept of general $g$-$eta$-monotone operator generalizing the general $(h,eta)$-monotone operator cite{arvar2, arvar1}, general $h-$ monotone operator cite{xiahuang} in banach spaces, and also generalizing $g$-$eta$-monotone operator cite{zhang}, $(a, eta)$-monotone operator cite{verma2}, $a$-monotone operator cite{verma0}, $(h, eta)$-monotone operator cite{fanghuang}...

We describe a time-dependent functional involving the relative entropy and $\dot{H}^1$ seminorm, which decreases along solutions to spatially homogeneous Landau equation with Coulomb potential. The study of this monotone sheds light on competition between dissipation nonlinearity for equation. It enables us obtain new results concerning regularity/blowup issues

We study the traveling wave front solutions for a two-dimensional periodic lattice dynamical system with monostable nonlinearity. We first show that there is a minimal speed such that a traveling wave solution exists if and only if its speed is above this minimal speed. Then we prove that any wave profile is strictly monotone. Finally, we derive the convergence of discretized minimal speed to t...

Abstract. First, we systematize earlier results on the global stability of the model ẋ + μx = f(x(· − τ)) of population growth. Second, we investigate the effect of delay on the asymptotic behavior when the nonlinearity f is a unimodal function. Our results can be applied to several population models [7, 9-13] because the function f does not need to be monotone or differentiable. Specifically, ...