相关论文: A new stability test for linear neutral differenti…

We examine the phenomenon of nonlinear stabilization, exhibiting a variety of related examples and counterexamples. For G\^ateaux differentiable maps, we discuss a mechanism of nonlinear stabilization, in finite and infinite dimensions,…

We study the existence of positive solutions on the half-line $[0,\infty)$ for the nonlinear second order differential equation \[ \bigl(a(t)x^{\prime}\bigr)^{\prime}+b(t)F(x)=0,\quad t\geq0, \] satisfying Dirichlet type conditions, say…

We consider a linear scalar delay differential equation (DDE), consisting of two arbitrary distributed time delays. We formulate necessary conditions for stability of the trivial solution which are independent of the distributions. For the…

Hyers-Ulam stability of the difference equation $ z_{n+1} = a_nz_n + b_n $ is investigated. If $ \prod_{j=1}^{n}|a_j| $ has subexponential growth rate, then difference equation generated by linear maps has no Hyers-Ulam stability. Other…

We prove well-posedness for doubly nonlinear parabolic stochastic partial differential equations of the form $dX_t-\text{div}\,\gamma(\nabla X_t)\,dt+\beta(X_t)\,dt\ni B(t,X_t)\,dW_t$, where $\gamma$ and $\beta$ are the two nonlinearities,…

In this paper, we will investigate the moment exponential stabilization of highly nonlinear hybrid stochastic differential delay equations. A periodically intermittent controller based on discrete time state observations with asynchronous…

We describe a situation where an unstable equilibrium in a $3 \times 3$ system of linear differential equations may be stabilized by introducing a delayed response, i.e. converting to a system of delayed differential equations. This…

In our manuscript, we develop a new approach for stability analysis of one-dimensional wave equation with time delay. The major contribution of our work is to develop a new method for spectral analysis. We derive sufficient and necessary…

We show the continuous dependence of solutions of linear nonautonomous second order parabolic partial differential equations (PDEs) with bounded delay on coefficients and delay. The assumptions are very weak: only convergence in the weak-*…

Discrete-time systems under aperiodic sampling may serve as a modeling abstraction for a multitude of problems arising in cyber-physical and networked control systems. Recently, model- and data-based stability conditions for such systems…

Derrick's theorem on the nonexistence of stable time-independent scalar field configurations [G. H. Derrick, J. Math. Phys. 5, 1252 (1964)] is generalized to finite systems of arbitrary dimension. It is shown that the "dilation" argument…

Recently, Horv\'ath, Song, and Terlaky [\emph{A novel unified approach to invariance condition of dynamical system, submitted to Applied Mathematics and Computation}] proposed a novel unified approach to study, i.e., invariance conditions,…

We consider a one-parameter family of beam equations with Hamiltonian non-linearity in one space dimension under periodic boundary conditions. In a unified functional framework we study the long time evolution of initial data in two…

This paper deals with an improvement of the "a-priori stability bounds" on the variation of the action variables and on the stability time obtained from a given Birkhoff normal form around the elliptic equilibrium point of an Hamiltonian…

The connection of function properties of solutions with exponential stability of linear impulsive differential equation $$\dot{x} (t) - \sum_{k=1}^m {A_k (t) x[h_k(t)]} = r(t),~ t \geq 0, x(\xi ) = \varphi (\xi),~ \xi < 0,$$ $$x(\tau_j) =…

Linear systems of neutral type are considered using the infinite dimensional approach. The main problems are asymptotic, non-exponential stability, exact controllability and regular asymptotic stabilizability. The main tools are the moment…

The Barzilai-Borwein (BB) step sizes have a profound impact on gradient descent methods. In this work, we propose two new gradient step sizes: one longer than the original long BB step size, and the other shorter than the original short BB…

This paper investigates projected Euler-Maruyama method for stochastic delay differential equations under a global monotonicity condition. This condition admits some equations with highly nonlinear drift and diffusion coefficients. We…

The logistic equation has many applications and is used frequently in different fields, such as biology, medicine, and economics. In this paper, we study the stability of a single-species logistic model with a general distribution delay…

We give sufficient conditions such that the exponential stability of the linearization of a non-linear system implies that the non-linear system is (locally) exponentially stable. One of these conditions is that the non-linear system is…