Linear stability theory of solitary waves arising from Hamiltonian systems with symmetry
This paper deals with variational inclusions of the form 0 ∈ φ(x) + F(x) where φ is a single-valued function admitting a second order Fréchet derivative and F is a set-valued map from to the closed subsets of . When a solution z̅ of the previous inclusion satisfies some semistability properties, we obtain local superquadratic or cubic convergent sequences.
On a closed convex set in with sufficiently smooth () boundary, the stop operator is locally Lipschitz continuous from into . The smoothness of the boundary is essential: A counterexample shows that -smoothness is not sufficient.
In this paper we generalize the class of admissible mappings as due by L. Górniewicz in 1976. Namely we define the notion of locally admissible mappings. Some properties and applications to the fixed point problem are presented.