This paper deals with global dispersive properties of Schrödinger equations with real-valued
potentials exhibiting critical singularities, where our class of potentials is more general than …

Abstract Laptev and Safronov (Commun Math Phys 292 (1): 29–54, 2009) conjectured an
inequality between the magnitude of eigenvalues of a non-self-adjoint Schrödinger operator …

Abstract Let 0< σ< n/2 0< σ< n/2 and H=(-Δ)^ σ+ V (x) H=(-Δ) σ+ V (x) be Schrödinger type
operators on R^ n R n with a class of scaling-critical potentials V (x), which include the Hardy …

This paper comprises two parts. We first investigate an L p-type of limiting absorption
principle for Schrödinger operators H=-Δ+ V on ℝ n (n≥ 3), ie, we prove the ϵ-uniform L …

We study the uniform resolvent estimates for Schrödinger operator with a Hardy-type
singular potential. Let LV=− Δ+ V (x) where Δ is the usual Laplacian on R n and V (x)= V 0 …

We extend a result of Davies and Nath (J Comput Appl Math 148 (1): 1–28, 2002) on the
location of eigenvalues of Schrödinger operators with slowly decaying complex-valued …

We study eigenvalues of non-self-adjoint Schrödinger operators on nontrapping
asymptotically conic manifolds of dimension n≥ 3. Specifically, we are concerned with the …

We prove uniform Sobolev estimates for the resolvent of Schrödinger operators with large
scaling-critical potentials without any repulsive condition. As applications, global-in-time …

We consider the resolvent estimates and properties of virtual states of the higher order
derivatives in one dimension, focusing on Schroedinger-type operators of degree $ N …

Let $ H=(-\Delta)^ m+ V $ be a higher-order elliptic operator on $ L^ 2 (R^ n) $ with a
general bounded decaying potential $ V $. This paper is devoted to consider the global Kato …