  Given a reflexive Banach space $X$, we consider a class of functionals $\Phi
\in C^1(X,\Re)$ that do not behave in a uniform way, in the sense that the map
$t \mapsto \Phi(tu)$, $t>0$, does not have a uniform geometry with respect to
$u\in X$. Assuming instead such a uniform behavior within an open cone $Y
\subset X \setminus \{0\}$, we show that $\Phi$ has a ground state relative to
$Y$. Some further conditions ensure that this relative ground state is the
(absolute) ground state of $\Phi$. Several applications to elliptic equations
and systems are given.
