Theoretical and applied problems of nonlinear analysis. (Теоретические и прикладные задачи нелинейного анализа.) (Russian) Zbl 1267.70010

Moscow: Rossiĭskaya Akademiya Nauk, Vychislitel’nyĭ Tsentr im. A. A. Dorodnitsyna (ISBN 978-5-91601-071-8/pbk). 207 p. (2012).
The book is devoted to the existence and stability analysis of planar central configurations in several variants of \(n\)-body problems of celestial mechanics. Additionally, the book considers the problems of linear and quadratic programming and criteria of optimal control.
The issue consists of 15 articles. V. A. Bereznev, Criterion of a sharpness of the convex polyheron (3-19); D. Yu. Karamzin, On extension of the classical optimal control theory to discontinuous trajectories (20-40); D. Yu. Karamzin, Regular zeros of quadratic mappings (41-52); A. F. Izmailov, E. I. Uskov, Effect of attraction of trajectories found by Newton-Lagrange method to Lagrange critical trajectories: a complete analysis in the one-dimensional case (53-71); E. A. Gebenikov, N. I. Zemtsova, Computer algebra methods in qualitative investigations of the Newtonian \(n\)-body problem (72-82); D. Yu. Karamzin, Maximum principle in the form by R.V.Gamkrelidze for optimal control problems with constrained phase coordinates (83-95); A. N. Dar’ina, On relations among regularity conditions for mixed complementary problems (96-105); D. Yu.Karamzin, Maximum principle for optimal control problems in the presence of mixed constraints (106-117); E. I. Uskov, Comparison of optimization algorithms by numerical methods (118-131); T. D. Berezneva, Rolling plans in a growth model with inhomogeneous labor forces (132-143); D. Yu. Karamzin, On perturbation of the optimal control problem (144-153); A. N. Dar’ina, On substantiation of the quadratic programming algorithm (154-160); N. I. Zemtsova, Stability of stationary solutions of the restricted 6-body problem in the case of equal frequences (161-170); V. A. Bereznev, Serial inclusion of constraints in quadratic programming problems (157-167); S. G. Zhuravlev, Proof of the existence theorem for planar central configurations with an axisymmetric ellipsoid at the centre in the \((4n+1)\)-body problem (184-205).
The issue will be useful to scientists and researches dealing with ordinary differential equations of celestial mechanics, central configurations and its stability, optimal control problems with constraints, problems of linear and quadratic programming, mathematical economics etc..


70F10 \(n\)-body problems
70K20 Stability for nonlinear problems in mechanics
90Cxx Mathematical programming
49Jxx Existence theories in calculus of variations and optimal control
91Bxx Mathematical economics
00B15 Collections of articles of miscellaneous specific interest


Zbl 1239.49023