Number of eigenvalues for dissipative Schrödinger operators under perturbation

AbstractIn this article, we prove that 0 is not an accumulating point of the eigenvalues for a class of dissipative Schrödinger operators H=−Δ+V(x) on Rn, n⩾2, with a complex-valued potential V(x) such that ℑV(x)⩽0 and ℑV≠0. If ℑV is sufficiently small, we show that N(V)=N(RV)+k, where k is the multiplicity of the zero resonance of the self-adjoint Schrödinger operator −Δ+RV and N(W) the number of eigenvalues of −Δ+W, counted according to their algebraic multiplicity