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March  2014, 13(2): 623-634. doi: 10.3934/cpaa.2014.13.623

## Infinitely many homoclinic solutions for damped vibration problems with subquadratic potentials

 1 Department of Mathematics, Tianjin Polytechnic University, Tianjin 300387, China 2 School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing 100875

Received  January 2013 Revised  April 2013 Published  October 2013

In this paper we investigate the existence of infinitely many homoclinic solutions for the following damped vibration problems \begin{eqnarray} \ddot q+A \dot q-L(t)q+W_q(t,q)=0, \end{eqnarray} where $A$ is an antisymmetric constant matrix, $L\in C(R,R^{n^2})$ is a symmetric and positive definite matrix for all $t\in R$, $W\in C^1(R\times R^n,R)$. The novelty of this paper is that, for the case that $W$ is subquadratic at infinity, we establish two new criteria to guarantee the existence of infinitely many homoclinic solutions for (DS) via the genus properties in critical point theory. Recent results in the literature are generalized and significantly improved.
Citation: Ziheng Zhang, Rong Yuan. Infinitely many homoclinic solutions for damped vibration problems with subquadratic potentials. Communications on Pure & Applied Analysis, 2014, 13 (2) : 623-634. doi: 10.3934/cpaa.2014.13.623
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