Constructive methods in the analysis of boundary value problems. Ed. and with a preface by V. A. Danilenko. (Конструктивные методы анализа краевых задач.) (Russian) Zbl 0786.34029
Kiev: Naukova Dumka. 96 p. (1990).
The author gives a constructive approach to the solution of the linear nonhomogeneous boundary value problem \(z'= A(t)z+ f(z)\) in \([a,b]\), \(\langle z^*,z\rangle=0\), where \(A\in C([0,1], M_ n({\mathbb R}))\) and \(z^*\in C^ 1[a,b]^*\), and also to the weakly perturbed nonlinear problem \(z'= A(t)z+ f(t)+\varepsilon g(z,t,\varepsilon)\). The approach is based on perturbation theory and the use of generalized Green matrices. This book is an interesting contribution to the theory of nonlinear oscillations of weakly perturbed boundary value problems.
Reviewer: J. Daneš (M.R. 92a:34020)
MSC:
34B15 | Nonlinear boundary value problems for ordinary differential equations |
34B27 | Green’s functions for ordinary differential equations |
34-02 | Research exposition (monographs, survey articles) pertaining to ordinary differential equations |