On boundary value problems for a nonlinear equation of gravitation theory. (O kraevykh zadachakh dlya odnogo neglinejnogo uravneniya teorii gravitatsii). (Russian) Zbl 0668.34001
Moskva: Izdatel’stvo Moskovskogo Universiteta. 86 p. R. 0.15 (1986).
Properties of solutions of the nonlinear ODE
\[
(1)\quad y''+\frac{2}{x}y'-\frac{(y')^ 2m}{y(y-2m)}-\frac{(y- 2m)}{y}[\frac{m}{y^ 2}+\frac{2y}{x^ 2}]=0
\]
in the theory of gravitation [E. I. Moiseev; V. A. Sadovnichii, On the solution of a nonlinear equation in theory of gravitation on the basis of Minkowski space, Moscow State Univ. Press (1984)] are here studied. This problem was proposed by A. A. Logunov with A. A. Vlasov [Minkowski space as a basics of physical theory of gravitation, Moscow State Univ. Press (1984)] for statistical spherically symmetric gravitational field. The uniqueness of solution and asymptotics of the solution at the inifinity are found for an external problem; for the internal problem the solvability is proved. This book is devoted to students and graduates studying in the field of applied mathematics and theoretical physics.
Reviewer: J.Tian
MSC:
| 34-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to ordinary differential equations |
| 34B99 | Boundary value problems for ordinary differential equations |
| 34A34 | Nonlinear ordinary differential equations and systems |
| 34E05 | Asymptotic expansions of solutions to ordinary differential equations |
| 83C45 | Quantization of the gravitational field |
