By means of a finite-dimensional reduction, we show a multiplicity result of semiclassical solutions to the singular nonlinear Schrodinger equation
where , , and are bounded potentials. Such solutions concentrate near (non-degenerate) local extrema or a (non-degenerate) manifold of stationary points of an auxiliary function related to the unperturbed electric field and the coefficient of the nonlinear term.
Submitted November 26, 2007. Published March 14, 2008.
Math Subject Classifications: 35J10, 35J60, 35J20, 35Q55, 58E05.
Key Words: Nonlinear Schrodinger equations; external magnetic field; singular potentials; semiclassical limit.
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| Sara Barile |
Dipartimento di Matematica, Politecnico di Bari
Via Orabona 4, I-70125 Bari, Italy
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