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Embedded eigenvalues and resonances of Schrödinger operators with two channels

Xue Ping Wang — 2007

Annales de la faculté des sciences de Toulouse Mathématiques

In this article, we give a necessary and sufficient condition in the perturbation regime on the existence of eigenvalues embedded between two thresholds. For an eigenvalue of the unperturbed operator embedded at a threshold, we prove that it can produce both discrete eigenvalues and resonances. The locations of the eigenvalues and resonances are given.

Analytic solutions of a second-order functional differential equation with a state derivative dependent delay

Jian-Guo SiXin-Ping Wang — 1999

Colloquium Mathematicae

This paper is concerned with a second-order functional differential equation of the form x ' ' ( z ) = x ( a z + b x ' ( z ) ) with the distinctive feature that the argument of the unknown function depends on the state derivative. An existence theorem is established for analytic solutions and systematic methods for deriving explicit solutions are also given.

On potentially K 5 - H -graphic sequences

Lili HuChunhui LaiPing Wang — 2009

Czechoslovak Mathematical Journal

Let K m - H be the graph obtained from K m by removing the edges set E ( H ) of H where H is a subgraph of K m . In this paper, we characterize the potentially K 5 - P 4 and K 5 - Y 4 -graphic sequences where Y 4 is a tree on 5 vertices and 3 leaves.

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