2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/225881In this article, we prove the finiteness of the number of eigenvalues for a class of Schrödinger operators $H = -Δ+ V(x)$ with a complex-valued potential $V(x)$ on $\bR^n$, $n \ge 2$. If $\Im V$ is sufficiently small, $\Im V \le 0$ and $\Im V \neq 0$, we show that $N(V) = N(\Re V)+ k$, where $k$ is the multiplicity of the zero resonance of the selfadjoint operator $-Δ+ \Re V$ and $N(W)$ the number of eigenvalues of $-Δ+ W$, counted according to their algebraic multiplicity.19 pagesSpectral TheoryMathematical Physics35J10, 35P15, 47A55text