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

作者：Cingolani Silvia^*; Jeanjean Louis; Secchi Simone

来源：ESAIM: Control, Optimisation and Calculus of Variations , 2009, 15(3): 653-675.

DOI：10.1051/cocv:2008055

• Nonlinear Schrodinger equations
• magnetic fields
• multi-peaks

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.

• 出版日期2009-9