Abstract'' Let
be a continuous function such that
defined by
is an increasing homeomorphism of
. Let us
also define the operator
Problems of this type, when properly formulated in the setting of
Orlicz - Sobolev spaces, leads to several difficulties connected
with the lack of homogeneity of and the structure of the
corresponding spaces (in general they may not be reflexive). Thus, for
example,
the functional naturally associated to
in problem
,
is in general neither everywhere defined nor a fortiori
.
This excludes the use of the standard Lagrange multiplier rule.