LAUSR

In this paper, we study the existence of multiple and infinite homoclinic solutions for the following perturbed dynamical systems $$\begin{aligned} \ddot{x}+A\cdot \dot{x}-L(t)\cdot x+\nabla W(t,x)=f(t), \end{aligned}$$x¨+A·x˙-L(t)·x+∇W(t,x)=f(t),where $$t\in {\mathbb R}, x\in {\mathbb R}^N,$$t∈R,x∈RN,A is an antisymmetric constant matrix, the matrix L(t) is not necessary positive definite for all $$t\in {\mathbb R}$$t∈R nor coercive, the nonlinearity $$W \in C^{1}(\mathbb {R}\times \mathbb {R}^{N},\mathbb {R})$$W∈C1(R×RN,R) involves a combination of superquadratic and subquadratic terms and is allowed to be sign-changing and $$f\in C({\mathbb R},{\mathbb R}^{N})\cap L^{2}({\mathbb R},{\mathbb R}^{N}).$$f∈C(R,RN)∩L2(R,RN). Recent results in the literature are generalized and significantly improved and some examples are also given to illustrate our main theoretical results.