R. Aebi, A SOLUTION TO SCHRODINGERS PROBLEM OF NONLINEAR INTEGRAL-EQUATIONS, Zeitschrift fur angewandte Mathematik und Physik, 46(5), 1995, pp. 772-792
A solution of Schrodinger's system of non-linear integral equations de
termines the rate function of a large deviation principle for kernels
with prescribed marginal distributions. This kind of large deviation p
rinciple has some meaning in quantum mechanics. Diffusion equations as
sociated with Schrodinger equations have typically transition function
s with singular creation and killing. Hence they provide measurable no
n-negative generally unbounded kernels which may vanish on sets with p
ositive measure and which can possess infinite mass. For Schrodinger s
ystems with such kernels, a solution is proved to exist uniquely in te
rms of a product measure. It is obtained from a variational principle
for the local adjoint of a product measure endomorphism. The generally
unbounded factors of the solution are characterized by integrability
properties.