## Journals

- Advances in Mathematics of Communications
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- Discrete & Continuous Dynamical Systems - A
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- Evolution Equations & Control Theory
- Inverse Problems & Imaging
- Journal of Computational Dynamics
- Journal of Dynamics & Games
- Journal of Geometric Mechanics
- Journal of Industrial & Management Optimization
- Journal of Modern Dynamics
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### Open Access Journals

DCDS

We prove the existence of periodic solutions in a second order
differential system with a singular potential of attractive or
repulsive type and forced periodically. The proof is based on a
Krasnoselskii fixed
point theorem for absolutely continuous operators on a Banach space,
and this makes possible to avoid any kind of "strong force" condition.

CPAA

Motivated by recent experiments studying
the dynamics of
configurations bearing a small number of vortices in
atomic Bose-Einstein condensates (BECs), we
illustrate that such systems can be accurately described by
ordinary differential equations (ODEs) incorporating the precession
and interaction dynamics of
vortices in
harmonic traps.
This dynamics is tackled in detail at the ODE level, both for
the simpler case of equal charge vortices,
and for the more complicated
(yet also experimentally relevant) case of opposite charge vortices.
In the former case, we identify the dynamics as being chiefly
quasi-periodic (although potentially periodic), while in the
latter, irregular dynamics may ensue
when suitable
external drive of the BEC cloud is also considered. Our analytical findings are
corroborated by numerical computations of the reduced ODE system.

DCDS

We study the existence of solution for the one-dimensional
$\phi$-laplacian equation $(\phi(u'))'=\lambda f(t,u,u')$ with
Dirichlet or mixed boundary conditions. Under general conditions,
an explicit estimate $\lambda_0$ is given such that the problem
possesses a solution for any $|\lambda|<\lambda_0$.

DCDS

We study Lyapunov stability for a given equation modelling the motion
of an earth satellite. The proof combines bilateral bounds of the solution
with
the theory of twist solutions.

DCDS

In this paper we study the
existence, multiplicity and stability of T-periodic solutions for
the equation $\left(\phi(x')\right)'+c\, x'+g(x)=e(t)+s.$

DCDS-B

Using Lie group theory and canonical transformations, we construct explicit solutions of nonlinear Schrödinger equations with spatially inhomogeneous nonlinearities. We present the general theory, use it to study different examples and use the qualitative theory of dynamical systems to obtain some properties of these solutions.

DCDS

We prove new results about the number of isolated periodic solutions of a
first order differential equation with a polynomial nonlinearity. Such results are applied to bound
the number of limit cycles of a family of planar polynomial vector fields which generalize the
so-called rigid systems.

DCDS-B

We study the existence and stability of periodic solutions of a differential equation that models the planar oscillations of a satellite in an elliptic orbit around its center of mass. The proof is based on a suitable version of Poincaré-Birkhoff theorem and the third order approximation method.

DCDS

We analyze the non-degeneracy of the linear $2n$-order differential
equation $u^{(2n)}+\sum\limits_{m=1}^{2n-1}a_{m}u^{(m)}=q(t)u$ with
potential $q(t)\in L^p(\mathbb{R}/T\mathbb{Z})$, by means of new
forms of the optimal Sobolev and Wirtinger inequalities. The results
is applied to obtain existence and uniqueness of
periodic solution for the prescribed nonlinear problem in the semilinear and superlinear case.

keywords:
superlinear
,
uniqueness
,
$2n$-order differential equation.
,
Non-degeneracy
,
semilinear

DCDS

For the Gylden-Meshcherskii-type problem with a
periodically cha-nging gravitational parameter, we prove the
existence of radially periodic solutions with high angular
momentum, which are Lyapunov stable in the radial direction.

## Year of publication

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