Special Variational Methods

Abstract

We saw in §12 that noncoercive problems

$$ - \Delta u + f({\text{x}},u) = 0\quad {\text{on}}\;{{\mathbb{R}}^{N}},u \to 0\quad \;{\text{as}}\;\left| {\text{x}} \right| \to \infty , $$

(13.1)

can be studied with the help of theorems on a conditional minimum if f is homogeneous. However such f are rare.