SYMMETRIC SEMICLASSICAL STATES TO A MAGNETIC NONLINEAR SCHRODINGER EQUATION VIA EQUIVARIANT MORSE THEORY
Por:
Cingolani S., Clapp M.
Publicada:
1 sep 2010
Resumen:
We consider the magnetic NLS equation (-epsilon i del + A(x))(2) u + V(x)u = K(x)|u|(p-2)u, x is an element of R(N), where N >= 3, 2 < p < 2* : = 2N/(N - 2), A : R(N) --> R(N) is a magnetic potential and V : R(N) --> R, K : R(N) --> R are bounded positive potentials. We consider a group G of orthogonal transformations of R(N) and we assume that A is G-equivariant and V, K are G-invariant. Given a group homomorphism tau : G --> S(1) into the unit complex numbers we look for semiclassical solutions u(epsilon): R(N) --> C to the above equation which satisfy u(epsilon)(gx) = tau(g)u(epsilon)(x) for all g is an element of G, x is an element of R(N). Using equivariant Morse theory we obtain a lower bound for the number of solutions of this type.
Filiaciones:
Cingolani S.:
Dipartimento di Matematica, Politecnico di Bari, via Orabona 4, 70125 Bari, Italy
Clapp M.:
Univ Nacl Autonoma Mexico, Inst Matemat, Mexico City 04510, DF, Mexico
Hybrid Gold
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