An axiomatic description of the Cauchy matrix (kernel of the integral representations of solutions) is given, the adjoint boundary value problem to the general linear boundary value problem is constructed, a method of the study of nonlinear boundary value problems for the solvability with the use of a priori inequality is developed. Jointly with N. V. Azbelev and L. F. Rakhmatullina, the basics of the general theory of functional differential equations are worked out. In colloboration with A. N. Rumyantsev, the constructive methods for the study of boundary value problems, including impulsive ones, are developed with the use of reliable computations; the theory and the imlementation of the reliable computing experiment are worked out, which are aimed to the study of wide classes of problems including some problems in economic dynamics.
Main publications:
Azbelev N. V., Maksimov V. P., and Rakhmatullina L. F. Introduction to the theory of linear functional differential equations. Atlanta: World Federation Publ., 1995.
Maksimov V. P., Rumyantsev A. N. The study of the solvability of boundary value problems for functional differential equations // Boundary Value Problems for Functional Differential Equations / ed. by J. Henderson. Singapore: World Scientific, 1995, 227–237.
