A multiplicity result for Chern-Simons-Schrodinger equation with a general nonlinearity

作者：Cunha Patricia L^*; d'Avenia Pietro; Pomponio Alessio; Siciliano Gaetano

来源：Nodea-Nonlinear Differential Equations and Applications, 2015, 22(6): 1831-1850.

DOI：10.1007/s00030-015-0346-x

• Chern-Simons gauge field
• Schrodinger equation
• Variational methods
• Radial solutions
• General nonlinearities

In this paper we give a multiplicity result for the following Chern-Simons-Schrodinger equation
-Delta u + 2qu integral(infinity)(vertical bar x vertical bar) u(2) (s)/s h(u)(s) ds + qu h(u)(2)(vertical bar x vertical bar)/vertical bar x vertical bar(2) = g(u), in R-2,
where h(u)(s) = integral(s)(0) tu(2)(tau) d tau, under very general assumptions on the nonlinearity g. In particular, for every n is an element of N, we prove the existence of (at least) n distinct solutions, for every q is an element of(0, q(n)), for a suitable q(n).

• 出版日期2015-12