The study deals with the theory of interior capacities of condensers
in a locally compact space, a condenser being treated here as a
countable, locally finite collection of arbitrary sets with the
sign $+1$ or $-1$ prescribed such that the closures of oppositely
signed sets are mutually disjoint. We are motivated by the known
fact that, in the noncompact case, the main minimum-problem of the
theory is in general unsolvable, and this occurs even under very
natural assumptions (e.g., for the Newtonian, Green, or Riesz
kernels in $\mathbb R^n$, $n\geqslant2$, and closed condensers of
finitely many plates). Therefore it was particularly interesting to
find statements of variational problems dual to the main
minimum-problem (and hence providing new equivalent definitions
to the capacity), but now always solvable (e.g., even for
nonclosed, unbounded condensers of infinitely many plates). For all
positive definite kernels satisfying Fuglede's condition of
consistency between the strong and vague ($={}$weak$*$) topologies,
problems with the desired properties are posed and solved. Their
solutions provide a natural generalization of the well-known notion
of interior equilibrium measures associated with a set. We give a
description of those solutions, establish statements on their
uniqueness and continuity, and point out their characteristic
properties. Such results are new even for classical kernels in
$\mathbb R^n$, which is important in applications.