Existence and multiplicity of Homoclinic solutions for the second order Hamiltonian systems

Details Existence and multiplicity of Homoclinic solutions for the second order Hamiltonian systems Existence and multiplicity of Homoclinic solutions for the second order Hamiltonian systems

2011-06-02

arxiv.org/abs/1106.0361v1

Mathematics

Dynamical Systems

published in International Mathematical Forum, Vol. 6, 2011, no. 4, 159 - 176

Scientific paper

In this paper we study the existence and multiplicity of homoclinic solutions for the second order Hamiltonian system $\ddot{u}-L(t)u(t)+W_u(t,u)=0$, $\forall t\in\mathbb{R}$, by means of the minmax arguments in the critical point theory, where $L(t)$ is unnecessary uniformly positively definite for all $t\in \mathbb{R}$ and $W_u(t, u)$ sastisfies the asymptotically linear condition.

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