MULTI-PEAK SOLUTIONS FOR MAGNETIC NLS EQUATIONS WITHOUT NON-DEGENERACY CONDITIONS

In this work we consider the magnetic NLS equation ((h) over bar / i del - A(x))(2) u + V(x)u - f(vertical bar u vertical bar(2))u = 0 in R-N (0.1) where N >= 3, A: R-N -> R-N is a magnetic potential, possibly unbounded, V: R-N -> R is a multi-well electric potential, which can vanish somewhere, f is a subcritical nonlinear term. We prove the existence of a semiclassical multi-peak solution u: R-N -> C to (0.1), under conditions on the nonlinearity which are nearly optimal.