We consider existence and qualitative properties of standing wave solutions
$$\Psi(x,t) = e^{-iEt/h}u(x)$$
to the nonlinear Schrödinger equation
$$ih\frac{\partial\psi} {\partial t} = -\frac{h^2}{2m}\Delta\psi+W(x)\psi-|\psi|^{p-1}\psi = 0$$
with E being a critical frequency in the sense that inf
$$_{x\in\mathbb{R}^N}W(x)=E$$
. We verify that if the zero set of W − E has several isolated points x
i
(
$$i=1,\ldots,m$$
) near which W − E is almost exponentially flat with approximately the same behavior, t...
