## Journals

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### Open Access Journals

DCDS

We introduce a new method for the boundedness problem of
semilinear Duffing equations at resonance. In particular, it can
be used to study a class of semilinear equations at resonance
without the polynomial-like growth condition. As an application,
we prove the boundedness of all the solutions for the equation
$\ddot{x}+n^2x+g(x)+\psi(x)=p(t)$
under the Lazer-Leach condition on $g$ and $p$, where $n\in \mathbb{N^+}$, $p(t)$ and $\psi(x)$ are periodic and $g(x)$ is bounded.

keywords:
periodic nonlinearity
,
Moser's theorem.
,
boundedness
,
Hamiltonian system
,
at resonance

DCDS-B

Quasi-periodic solutions of the Lotka-Volterra competition systems with quasi-periodic perturbations

In this paper, we prove the existence of positive quasi-periodic
solutions for the Lotka-Volterra competition systems with
quasi-periodic coefficients by KAM technique. The result shows
that, in most case, quasi-periodic solutions exist for
sufficiently small quasi-periodic perturbations of the autonomous
Lotka-Volterra systems. Moreover, these quasi-periodic solutions
will tend to an equilibrium of the autonomous Lotka-Volterra
systems.

## Year of publication

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