Sublevel sets and global minima of coercive functionals and local minima of their perturbations
Abstract
The aim of the present paper is essentially to prove that if $\Phi$ and $\Psi$ are two sequentially weakly lower semicontinuous functionals on a reflexive real Banach space and if $\Psi$ is also continuous and coercive, then then following conclusion holds: if, for some $r > \inf_X \Psi$, the weak closure of the set $\Psi^{1}(]\infty, r[)$ has at least $k$ connected components in the weak topology, then, for each $\lambda > 0$ small enough, the functional $\Psi + \lambda\Phi$ has at least $k$ local minima lying in $\Psi^{1}(]\infty, r[)$.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 February 2004
 arXiv:
 arXiv:math/0402444
 Bibcode:
 2004math......2444R
 Keywords:

 Mathematics  Optimization and Control;
 35J20
 EPrint:
 12 pages