## Journals

- Advances in Mathematics of Communications
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- Discrete & Continuous Dynamical Systems - A
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- Evolution Equations & Control Theory
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- 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

This paper is devoted to the existence and multiplicity of periodic
and subharmonic solutions for a superlinear
Duffing equation with a singularity. In this manner,
various preceding theorems are improved and sharpened.
Our proof is based on a generalized version of the Poincaré-Birkhoff twist
theorem.

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-B

An experimental conjecture on the existence of
positive periodic solutions for the Brillouin electron beam focusing
system $x''+a(1+\cos2t)x=\frac{1}{x}$
for $0 < a < 1$ is proved, using a topological degree theorem by Mawhin.

## Year of publication

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