  We consider the equation $\Delta_x u+u_{yy}+f(u)=0,\
x=(x_1,\dots,x_N)\in\mathbb{R}^N,\ y\in \mathbb{R},$ where $N\geq 2$ and $f$ is
a sufficiently smooth function satisfying $f(0)=0$, $f'(0)<0$, and some natural
additional conditions. We prove that the equation possesses uncountably many
positive solutions (disregarding translations) which are radially symmetric in
$x'=(x_1,\dots,x_{N-1})$ and decaying as $|x'|\to\infty$, periodic in $x_N$,
and quasiperiodic in $y$. Related theorems for more general equations are
included in our analysis as well. Our method is based on center manifold and
KAM-type results.
