相关论文: Bohl-Perron type stability theorems for linear dif…

We prove that solutions to Cauchy problems related to the $p$-parabolic equations are stable with respect to the nonlinearity exponent $p$. More specifically, solutions with a fixed initial trace converge in an $L^q$-space to a solution of…

The problem considered in the paper is exponential stability of linear equations and global attractivity of nonlinear non-autonomous equations which include a non-delay term and one or more delayed terms. First, we demonstrate that…

The existence of sufficiently many finite order meromorphic solutions of a differential equation, or difference equation, or differential-difference equation, appears to be a good indicator of integrability. In this paper, we investigate…

In this paper, we study the $L^p$-asymptotic stability with $p\in (1,\infty)$ of the one-dimensional nonlinear damped wave equation with a localized damping and Dirichlet boundary conditions in a bounded domain $(0,1)$. We start by…

In this paper we consider a fourth order nonlinear parabolic delayed problem modelling a quasi-instantaneous turn-over of linkages in the context of cell-motility. The model depends on a small parameter $\epsilon$ which represents a typical…

This paper combines the decay of high modes with the smallness introduced by high orders, leading to a normal form lemma for infinite-dimensional Hamiltonian systems under ultra-differentiable regularity. We prove the sub-exponential…

We derive a consistency result, in the $L_1$-sense, for incomplete U-statistics in the non-standard case where the kernel at hand has infinite second-order moments. Assuming that the kernel has finite moments of order $p(\geq 1)$, we obtain…

We prove stability for a class of heterogeneous catalysis models in the $L_p$-setting. We consider a setting in a finite three-dimensional pore of cylinder-like geometry, with the lateral walls acting as a catalytic surface. Under a…

In this work, we study the dynamics of a spatially heterogeneous single population model with the memory effect and nonlinear boundary condition. By virtue of the implicit function theorem and Lyapunov-Schmidt reduction, spatially…

The existence of breather type solutions, i.e., periodic in time, exponentially localized in space solutions, is a very unusual feature for continuum, nonlinear wave type equations. Following an earlier work [Comm. Math. Phys. {\bf 302},…

In this paper, We study an one--dimensional morphogenesis model considered by C. Stinner et al. in (Math. Meth. Appl. Sci. 2012,35 (445-465). Under homogeneous boundary conditions, we prove the existence of nonconstant positive steady…

We study the asymptotic behavior of a bounded solution of an inhomogeneous delay linear difference equation in a Banach space by using the spectrum of bounded sequences. We get a significant extension of excellent results in [1]. A new…

In this paper, we investigate the rapid stabilizability of linear infinite-dimensional control systems with constant delays. Under the assumptions that the state operator generates an immediately compact semigroup and that the delay…

Assuming as hypotheses the results proved numerically by Chang et al. \cite{Chang} for the exponent $p\in (3,5)$, we prove that some of the ground states of the nonlinear Schr\"odinger equation (NLS) with pure power nonlinearity of exponent…

This paper investigates the robustness of exponential stability of a class of switched systems described by linear functional differential equations under arbitrary switching. We will measure the stability robustness of such a system,…

This paper studies exponential stability properties of a class of two-dimensional (2D) systems called differential repetitive processes (DRPs). Since a distinguishing feature of DRPs is that the problem domain is bounded in the "time"…

Linear scalar differential equations with distributed delays appear in the study of the local stability of nonlinear differential equations with feedback, which are common in biology and physics. Negative feedback loops tend to promote…

We consider an inverse problem for the nonlinear Boltzmann equation with a time-dependent kernel in dimensions $n\ge 2$. We establish a logarithm-type stability result for the collision kernel from measurements under certain additional…

We prove nonlinear stability of line soliton solutions of the KP-II equation with respect to transverse perturbations that are exponentially localized as $x\to\infty$. We find that the amplitude of the line soliton converges to that of the…

This article is focused on two related topics within the study of partial differential equations (PDEs) that illustrate a beautiful connection between dynamics, topology, and analysis: stability and spatial dynamics. The first is a property…