  The present paper is an extension of 'cond-mat/0312673'. The construction of
a hybrid discrete-continuous model of layered superconductors is presented. The
model bases on the classic Lawrence-Doniach scenario with admitting, however,
long-range interactions between atomic planes. Moreover, apart from Josephson
couplings they involve the proximity effects. The range of interactions can, in
principle, be arbitrary large. The solutions corresponding to the range K=2 are
found. The mechanism of enhancement of superconductivity caused by the
proximity effect and the presence of higher Josephson couplings is shown. The
physical meaning of coupling constants, with particular attention paid to their
sign, is discussed. For the case K=2 the interpretation in terms of microscopic
interactions between Cooper pairs in different planes, as well as the relation
to experimentally measurable quantities, such as the out-of-plane effective
mass and bandwidth, is given.
