Related papers: Are nonlocal Lagrangian systems fatally unstable?
Working with a general class of linear Hamiltonian systems with at least one singular boundary condition, we show that renormalized oscillation results can be obtained in a natural way through consideration of the Maslov index associated…
We extend the notion of orbital stability to systems of nonlinear Schrodinger equations, then we prove this property under suitable assumptions of the local nonlinearity involved.
We analyze the stability properties of Lur'e systems with piecewise continuous nonlinearities by exploiting the notion of set-valued Lie derivative for Lur'e-Postnikov Lyapunov functions. We first extend an existing result of the literature…
We introduce the notion of Lyapunov exponents for random dynamical systems, conditioned to trajectories that stay within a bounded domain for asymptotically long times. This is motivated by the desire to characterize local dynamical…
The main result of the paper is a global asymptotic stability result for solutions to the Lifschitz-Slyozov-Wagner (LSW) system of equations. This extends some local asymptotic stability results of Niethammer-Vel\'{a}zquez (2006). The…
We prove exponential stability theorems of Nekhoroshev type for motion in the neighbourhood of an elliptic fixed point in Hamiltonian systems having an additional transverse component of arbitrary dimension.
The paper deals with the problem of existence of a convergent "strong" normal form in the neighbourhood of an equilibrium, for a finite dimensional system of differential equations with analytic and time-dependent non-linear term. The…
In two recent papers necessary and sufficient conditions for a given system of second-order ordinary differential equations to be of Lagrangian form with additional dissipative forces were derived. We point out that these conditions are not…
Motivated by the considerable success of alternative theories of gravity, we consider the toy model of a higher derivative Lagrangian theory, namely the Pais-Uhlenbeck oscillator studied in a recent paper by Hawking-Hertog. Its Euclidean…
While there have been many studies examining the stability of hierarchical triple systems, the meaning of ``stability'' is somewhat vague and has been interpreted differently in previous literatures. The present paper focuses on ``Lagrange…
We prove regularity estimates for time derivatives of a large class of nonlinear parabolic partial differential systems. This includes the instationary (symmetric) p-Laplace system and models for non Newtonien fluids of powerlaw or Carreau…
The topic of this manuscript is the stability analysis of continuous-time switched nonlinear systems with constraints on the admissible switching signals. Our particular focus lies in considering signals characterized by upper and lower…
We analyse the development of instability in the framework of nonlinear electrodynamics based on the Maxwell's equations without approach of slowly varying amplitudes and phases. The action is chosen from the Heisenberg-Euler Lagrangian,…
The paper deals with the problem of the sampled data feedback stabilization for autonomous nonlinear systems. The corresponding results extend those obtained in earlier works by the same authors. The sufficient conditions we establish are…
We prove Lyapunov instability for cases in which the local minimum of the potential energy is reached on a hypersurface of the configuration space. In contrast to the known results in this direction, which hold for potentials satisfying…
We investigate the stability properties of an abstract class of semi-linear systems. Our main result establishes rational rates of decay for classical solutions assuming a certain non-uniform observability estimate for the linear part and…
We extend Lyapunov--type Mittag--Leffler stability analysis for fuzzy nonlinear fractional differential equations (Caputo sense) and introduce a family of stronger, broadly applicable stability results. In particular, we develop (i) uniform…
A generalized Lyapunov method is outlined which predicts global stability of a broad class of dissipative dynamical systems. The method is applied to the complex Lorenz model and to the Navier-Stokes equations. In both cases one finds…
We investigate to what extent a suitably chosen system Hamiltonian can counteract local dissipative processes and preserve entanglement in the stationary state. The results determine prospects and limitations of dissipative state…
The paper analyzes a Lagrangian system which is controlled by directly assigning some of the coordinates as functions of time, by means of frictionless constraints. In a natural system of coordinates, the equations of motions contain terms…