Given a reflexive Banach space X, we consider a class of functionals Φ∈C1(X,ℜ) that do not behave in a uniform way, in the sense that the map
t↦Φ(tu), t>0, does not have a uniform geometry with respect to
u∈X. Assuming instead such a uniform behavior within an open cone Y⊂X∖{0}, we show that Φ has a ground state relative to
Y. Some further conditions ensure that this relative ground state is the
(absolute) ground state of Φ. Several applications to elliptic equations
and systems are given