Action as function of period for ground states of semilinear elliptic equations

Abstract

The ground states of semilinear elliptic equations are considered. We make the conjecture that the set of ground states forms a finite-dimensional manifold. We analyse this conjecture indirectly. More precisely, we investigate a restriction of the associated functional of action on the set of ground states. On this approach some new finite-dimensional properties of the functional of action and of the ground states are deduced.