Concentration of solutions of equations of nonlinear Schrödinger type with vector potential: infinite-bump solutions and non-degeneracy

Abstract

The equation –ε2Δu+F(V(x),u) = 0 is studied over all of ℝn, and solutions are constructed that concentrate at an infinite set asε→ 0. The functionV(x) is vector valued. This advances previous studies in whichV(x) was scalar valued.