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摘要
By means of a finite-dimensional reduction, we show a multiplicity result of semiclassical solutions u : R-N -> C to the singular nonlinear Schrodinger equation
(epsilon/i del - A(x))(2)u + u + (V(x) - gamma(epsilon)W(x))u = K(x)vertical bar u vertical bar(p-1)u, x is an element of R-N,
where N >= 2, 1 < p < 2* - 1, A(x), V(x) and K(x) are bounded potentials. Such solutions concentrate near (non-degenerate) local extrema or a (non-degenerate) manifold of stationary points of an auxiliary function A related to the unperturbed electric field V(x) and the coefficient K(x) of the nonlinear term.
- 出版日期2008
