Opérateurs de temps-retard dans la théorie de la diffusion
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.
We correct an error in the normalizing constant of resonant states.
For Schrödinger operator on Riemannian manifolds with conical end, we study the contribution of zero energy resonant states to the singularity of the resolvent of near zero. Long-time expansion of the Schrödinger group is obtained under a non-trapping condition at high energies.
This paper is concerned with a second-order functional differential equation of the form 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.
Let G be a 2-connected planar graph with maximum degree Δ such that G has no cycle of length from 4 to k, where k ≥ 4. Then the total chromatic number of G is Δ +1 if (Δ,k) ∈ {(7,4),(6,5),(5,7),(4,14)}.
Let be the graph obtained from by removing the edges set of where is a subgraph of . In this paper, we characterize the potentially and -graphic sequences where is a tree on 5 vertices and 3 leaves.
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