Number of eigenvalues for a class of non-selfadjoint Schr\"odinger operators

arXiv0902.0921MaRDI QIDQ6212653

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Publication date: 5 February 2009

Abstract: In this article, we prove the finiteness of the number of eigenvalues for a class of Schr"odinger operators $H=-Delta+V(x)$ with a complex-valued potential $V(x)$ on $$, $nge2$. If $ImV$ is sufficiently small, $ImVle0$ and $ImVeq0$, we show that $N(V)=N(ReV)+k$, where $k$ is the multiplicity of the zero resonance of the selfadjoint operator $-Delta+ReV$ and $N(W)$ the number of eigenvalues of $-Delta+W$, counted according to their algebraic multiplicity.

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