Codice  QDD 114 
Titolo  A remark on natural constraints in variational methods and an application to superlinear SchrÃ¶dinger systems 
Data  20111214 
Autore/i  Noris, B.; Verzini, G. 
Link  Download full text 
Abstract  For a regular functional J defined on a Hilbert space X, we consider the set N of points x of X such that the projection of the gradient of J at x onto a closed linear subspace V(x) of X vanishes. We study sufficient conditions for a constrained critical point of J restricted to N to be a free critical point of J, providing a unified approach to different natural constraints known in the literature, such as the BirkhoffHestenes natural isoperimetric conditions and the Nehari manifold. As an application, we prove multiplicity of solutions to a class of superlinear SchrÃ¶dinger systems on singularly perturbed domains.

