Global Persistence of the Unit Eigenvectors of Perturbed Eigenvalue Problems in Hilbert Spaces: The Odd Multiplicity Case

We study the persistence of eigenvalues and eigenvectors of perturbed eigenvalue problems in Hilbert spaces. We assume that the unperturbed problem has a nontrivial kernel of odd dimension and we prove a Rabinowitz-type global continuation result. The approach is topological, based on a notion of degree for oriented Fredholm maps of index zero between real differentiable Banach manifolds.

Threat of Limited Nuclear War

The article addresses the contemporary risks of limited nuclear war and its threat for societies. It offers a critical analysis based on the difference between the strategy of a global destructive war following classical application of standard nuclear weapons, on the one hand, and the new political military plan of limited nuclear war, without its global continuation, on the other. First, the article explains the problems connected with the new US strategic documents pursuing limited nuclear war. Second, within this context of the risks of limited nuclear war, it explains conflicts of political (potentially democratic), corporate, and technical military interests in global capitalism which can lead to the limited nuclear war. Third, it concludes by clarifying the historical trajectory of debates concerning the strategies of possible nuclear war, and stresses the current real danger of limited nuclear war and its possible global escalation.