  In this paper, we are concerned with quasilinear Dirichlet problem $$ \left\{
\aligned &-\Big(\frac{u'(x)}{\sqrt{1+\kappa (u'(x))^2}}\Big)'=\lambda u(x), \ \
  \ \ \ 0<x<1,\\ &u(0)= u(1)=0,\\ \endaligned \right. \eqno (P) $$ where
$\kappa\in (-\infty, 0)\cup (0, \infty)$ is a constant. We show that any
nontrivial solution $ u$ of (P) has only finite many of simple zeros in
$[0,1]$, all of humps of $u$ are same, and the first hump is symmetric around
the middle point of its domain. We also describe the global structure of the
set of nontrivial solutions of (P).
