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A new delay equation is introduced to describe the punctuated evolution of complex nonlinear systems. A detailed analytical and numerical investigation provides the classification of all possible types of solutions for the dynamics of a…
Point-like topological defects are singular configurations that occur in a variety of in and out of equilibrium systems with two-dimensional orientational order. As they are associated with a nonzero circuitation condition, the presence of…
We study a nonlinear recombination model from population genetics as a combinatorial version of the Kac-Boltzmann equation from kinetic theory. Following Kac's approach, the nonlinear model is approximated by a mean field linear evolution…
Using the damped pendulum system we introduce the averaging method to study the periodic solutions of a dynamical system with small perturbation. We provide sufficient conditions for the existence of periodic solutions with small amplitude…
We consider a one dimensional evolution problem modeling the dynamics of an acoustic field coupled with a set of mechanical oscillators. We analyze solutions of the system of ordinary and partial differential equations with time-dependent…
We study a non-autonomous, non-linear evolution equation on the space of operators on a complex Hilbert space. We specify assumptions that ensure the global existence of its solutions and allow us to derive its asymptotics at temporal…
Motivated by recent experiments in optics and atomic physics, we derive an averaged nonlinear partial differential equation describing the dynamics of the complex field in a nonlinear Schroedinger model in the presence of a periodic…
We apply functional analytical and variational methods in order to study well-posedness and qualitative properties of evolution equations on product Hilbert spaces. To this aim we introduce an algebraic formalism for matrices of…
We consider contractive systems whose trajectories evolve on a compact and convex state-space. It is well-known that if the time-varying vector field of the system is periodic then the system admits a unique globally asymptotically stable…
We study the asymptotic behavior of the trajectory of a nonautonomous evolution equation governed by a quasi-nonexpansive operator in Hilbert spaces. We prove the weak convergence of the trajectory to a fixed point of the operator by…
It was shown recently that the constraints on the initial data for Einstein's equations may be posed as an evolutionary problem [9]. In one of the proposed two methods the constraints can be replaced by a first order symmetrizable…
We prove existence and uniqueness results for (mild) solutions to some non-linear parabolic evolution equations with a rough forcing term. Our method of proof relies on a careful exploitation of the interplay between the spatial and time…
Nonlinear control-affine systems described by ordinary differential equations with bounded measurable input functions are considered. The solvability of general boundary value problems for these systems is formulated in the sense of…
The not necessarily unitary evolution operator of a finite dimensional quantum system is studied with the help of a projection operators technique. Applying this approach to the Schr\"odinger equation allows the derivation of an alternative…
This paper proposes an abstract theory concerned with dynamical systems generated by doubly nonlinear evolution equations governed by subdifferential operators with non-monotone perturbations in a reflexive Banach space setting. In order to…
In this paper, we study the existence and uniqueness of periodic solutions of the differential equation of the form . Here, we obtain some sufficient conditions which guarantee the existence of periodic solutions. This equation is a quite…
A thin and narrow rectangular plate having the two short edges hinged and the two long edges free is considered. A nonlinear nonlocal evolution equation describing the deformation of the plate is introduced: well-posedness and existence of…
We consider a linear differential system of Mathieu equations with periodic coefficients over periodic closed orbits and we prove that, arbitrarily close to this system, there is a linear differential system of Hamiltonian damped Mathieu…
We consider the nonlinear nonlocal beam evolution equation introduced by Woinowsky- Krieger. We study the existence and behavior of periodic solutions: these are called nonlinear modes. Some solutions only have two active modes and we…
A boundary value problem related to a third- order parabolic equation with a small parameter is analized. This equation models the one-dimensional evolution of many dissipative media as viscoelastic fluids or solids, viscous gases,…