This paper investigate the following damped nonlinear impulsive differential equations.
$$ \begin{gathered} - u''(t) + p(t)u'(t) + q(t)u(t) = f(t,u(t)),\;a.e.\;t \in [0,T], \hfill \\ \Delta u'(t_{j} ) = I_{j} (u(t_{j} )),\begin{array}{*{20}c} {} & {j = 1,2, \ldots ,m,} \\ \end{array} \hfill \\ u(0) = u(T) = 0. \hfill \\ \end{gathered} $$
Applying fountain theorem and a new analytical approach, we obtain that the aforementioned problem has infinitely many solutions under the local superlinear condition
$$\mathop {\lim }\nolimits_{\left| u \right| \to + \infty } \frac{{\int_{0...
