
Volume 5
M. A. Krasnosel'skij, E. A. Lifshits, A. V. Sobolev
Positive Linear Systems. The Method of Positive Operators
362 p., soft cover, ISBN 3885384051, EUR 45.00, 1989
The book is concerned with methods for studying systems and problems whose mathematical
description leads to equations involving positive operators with respect to some partial
ordering.
The first chapter introduces basic notions as partial ordering, various classes of cones
and their geometry, ideally convex sets and smoothness points. The second presents
applications to spectral problems involving principal eigenvalues and eigendirections,
peripheral eigenvalues, focussing and acute operators, and oscillation theorems. The
third chapter studies iteration procedures and methods for obtaining estimates for
spectral radii and spectral margins, and a posteriori estimates in eigenvector problems.
The last chapter is concerned with some applications to forced oscillation problems in
automatic control systems, including their construction by means of the harmonic balance
method, as well as with stability and absolute stability problems.
