摘要：In this paper, we study a class of damped vibration systems, u ¨ ( t ) + B u ˙ ( t ) − L ( t ) u ( t ) + ∇ W ( t , u ( t ) ) = 0 , ∀ t ∈ R , $$ \ddot{u}(t)+B\dot{u}(t)-L(t)u(t)+\nabla W\bigl(t,u(t)\bigr)=0, \quad \forall t \in \mathbb{R}, $$ where W ( t , u ) $W(t,u)$ is of indefinite sign. By using a critical point theorem of Ding, we establish a new criterion to guarantee that the above system has infinitely many nontrivial homoclinic orbits under the assumption that W ( t , u ) $W(t,u)$ is asymptotically quadratic or subquadratic as u → ∞ $ u \rightarrow\infty$ . Recent results in the literature are generalized and significantly improved.
