I am reading this paper and the authors stated
it is easy to construct examples of $Q(x)$ for which none of the above criteria are satisfied and condition $(Q)$ holds.
on page $569$.
The $(Q)$ condition is
$Q(x) \geq 0$ in $\mathbb{R}^N$ and there exist some points $a^1, \cdots, a^k$ in $\mathbb{R}^N$ such that $Q(a^j)$ are strict maximums and satisfy $$Q(a^j) = Q_{\text{max}} \equiv \ \text{Max} \ \{ Q(x) ; x \in \mathbb{R}^N \} > 0, j = 1, \cdots, k.$$
The other conditions are in the final of the page $568$.
I am having difficult to define such function $Q$, then I would like to receive some intuition about how to construct it. All I could think in order to define such function is to construct a function like this
such that $Q$ behaves periodically as $|x| \rightarrow \infty$.
Thanks in advance!