This paper deals with the existence of infinitely many
solutions for the boundary value problem
$-( | u' | ^{p-2}u')' + \varepsilon |u|^{p-2}u=
\nabla F(t,u), $ in $(0,T)$,
$((|u'|^{p-2}u')(0), $
$ -(|u'|^{p-2}u')(T))$ $\in \partial j(u(0), u(T)),$
where $\varepsilon \geq
0$, $p \in (1, \infty)$ are fixed, the convex function
$j:\mathbb R^N \times \mathbb R^N \to (- \infty , +\infty ]$ is
proper, even, lower semicontinuous and $F:(0,T) \times
\mathbb R^N \to \mathbb R $ is a Carathéodory mapping,
continuously differentiable and even with respect to the second
variable.
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