1. CMB 2017 (vol 60 pp. 422)
 Tang, Xianhua

New Superquadratic Conditions for Asymptotically Periodic SchrÃ¶dinger Equations
This paper is dedicated to studying the
semilinear SchrÃ¶dinger equation
$$
\left\{
\begin{array}{ll}
\triangle u+V(x)u=f(x, u), \ \ \ \ x\in {\mathbf{R}}^{N},
\\
u\in H^{1}({\mathbf{R}}^{N}),
\end{array}
\right.
$$
where $f$ is a superlinear, subcritical nonlinearity. It focuses
on the case where
$V(x)=V_0(x)+V_1(x)$, $V_0\in C(\mathbf{R}^N)$, $V_0(x)$ is 1periodic
in each of $x_1, x_2, \ldots, x_N$ and
$\sup[\sigma(\triangle +V_0)\cap (\infty, 0)]\lt 0\lt \inf[\sigma(\triangle
+V_0)\cap (0, \infty)]$,
$V_1\in C(\mathbf{R}^N)$ and $\lim_{x\to\infty}V_1(x)=0$. A new superquadratic
condition is obtained,
which is weaker than some well known results.
Keywords:SchrÃ¶dinger equation, superlinear, asymptotically periodic, ground state solutions of NehariPankov type Categories:35J20, 35J60 

2. CMB 2011 (vol 55 pp. 858)
 von Renesse, MaxK.

An Optimal Transport View of SchrÃ¶dinger's Equation
We show that the SchrÃ¶dinger equation is a lift of Newton's third law
of motion $\nabla^\mathcal W_{\dot \mu} \dot \mu = \nabla^\mathcal W F(\mu)$ on
the space of probability measures, where derivatives are taken
with respect to the Wasserstein Riemannian metric. Here the potential
$\mu \to F(\mu)$ is the sum of the total classical potential energy $\langle V,\mu\rangle$
of the extended system
and its Fisher information
$ \frac {\hbar^2} 8 \int \nabla \ln \mu ^2
\,d\mu$. The precise relation is established via a wellknown
(Madelung) transform which is shown to be a symplectic submersion
of the standard symplectic
structure of complex valued functions into the
canonical symplectic space over the Wasserstein space.
All computations are conducted in the framework of Otto's formal
Riemannian calculus for optimal transportation of probability
measures.
Keywords:SchrÃ¶dinger equation, optimal transport, Newton's law, symplectic submersion Categories:81C25, 82C70, 37K05 
