Solitary waves solutions of a nonlinear Schroedinger equation
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The aim of this note is to prove the existence of standing waves solutions of the following nonlinear Schrödinger equation I(∂ψ/∂t)=−Δψ+V(x)ψ+εN(ψ), where NM is a nonlinear differential operator. In  and  Benci and the authors proved the existence of a finite number of solutions (µ(e), u(e)) of the eigenvalue problem −Δu+V(x)u+εN(u)=μu (Pε) where N(u) = −Δpu + W′(u). The number of solutions can be as large as one wants. Since W is singular in a point these solutions are characterized by a topological invariant, the topological charge. A min-max argument is used.