  This article is dedicated to establishing a novel approach to the
cosmological constant, in which it is treated as an eigenvalue of a certain
Sturm--Liouville problem. The key to this approach lies in the proper
formulation of physically relevant boundary conditions. Our suggestion in this
regard is to utilize the ``holographic boundary condition'', under which the
cosmological horizon can only bear a natural (i.e., non-fractional) number of
bits of information. Under this framework, we study the general d-dimensional
problem and derive the general formula for the discrete spectrum of a positive
energy density of vacuum. For the particular case of two dimensions, the
resultant problem can be analytically solved in the degenerate hypergeometric
functions, so it is possible to define explicitly a self-action potential,
which determines the fields of matter in the model. We conclude the article by
taking a look at the d-dimensional model of a fractal horizon, where the
Bekenstein's formula for the entropy gets replaced by the Barrow entropy. This
gives us a chance to discuss a recently realized problem of possible existence
of naked singularities in the $D\neq 3$ models.
