Small perturbations for a Duffing-like evolution equation involving non-commuting operators

Evolution Equation for Non-linear Cosmological Perturbations

We present a novel approach, based entirely on the gravitational potential, for studying the evolution of non-linear cosmological matter perturbations. Starting from the perturbed Einstein equations, we integrate out the non-relativistic degrees of freedom of the cosmic fluid and obtain a single closed equation for the gravitational potential. We then verify the validity of the new equation by ...

Existence of homoclinic orbits for asymptotically periodic systems involving Duffing-like equation

we are concerned with perturbations of the Hamiltonian system of the type c L(t)q + W&, q) = 0, t E R, WI where q = (ql, , qN) E WN, W E C1(W x WN,R), and L(t) E C(W,WN2) is a positive definite symmetric matrix. Variational arguments are used to prove the existence of homoclinic solutions for system (HS). @ 2003 Elsevier Science Ltd. All rights reserved. KeywordsHomoclinic orbits, Duffing equat...

A non-autonomous kind of Duffing equation

We study the periodic solutions of the following kind of non-autonomous Duffing differential equation ÿ+ay− εy = εh(t, y, ẏ), with a > 0, ε a small parameter and h a C2 function in its variables.

Functional Calculus for Non-Commuting Operators

Ela Polynomial Inequalities for Non-commuting Operators

We prove an inequality for polynomials applied in a symmetric way to non-commuting operators.