In this paper we study the existence of concentrated solutions of the nonlinear field equation
where , , , the potential is positive and radial, and is an appropriate singular function satisfying a suitable symmetric property. Provided that is sufficiently small, we are able to find solutions with a certain spherical symmetry which exhibit a concentration behaviour near a circle centered at zero as . Such solutions are obtained as critical points for the associated energy functional; the proofs of the results are variational and the arguments rely on topological tools. Furthermore a penalization-type method is developed for the identification of the desired solutions.
Submitted May 15, 2000. Published November 16, 2000.
Math Subject Classifications: 35J20, 35J60.
Key Words: nonlinear Schrodinger equations, topological charge, existence, concentration.
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| Teresa D'Aprile |
Scuola Normale Superiore
Piazza dei Cavalieri 7, 56126 Pisa, Italy
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