  In this paper we study the Lawrence-Doniach model for layered
superconductors, for a sample with finite width subjected to a magnetic field
parallel to the superconducting layers. We provide a rigorous analysis of the
energy minimizers in the limit as the coupling between adjacent superconducting
layers tends to zero. We identify a unique global minimizer of the Gibbs free
energy in this regime ("vortex planes"), and reveal a sequence of first-order
phase transitions by which Josephson vortices are nucleated via the boundary.
The small coupling limit is studied via degenerate perturbation theory based on
a Lyapunov-Schmidt decomposition which reduces the Lawrence-Doniach system to a
finite-dimensional variational problem. Finally, a lower bound on the radius of
validity of the perturbation expansion (in terms of various parameters
appearing in the model) is obtained.
