The conception of extended operator derivative is proved. The exemples of non-differentiable operators with extended derivative are bringing. The theorem of extended differentiability of inverse function is proved. It is indicate, that differential dependence of the resolution of the boundary problem for a nonlinear partial equation to avaible component is progressively degraded with the augmentation of nonlinearity coefficient and set dimension; it is depend also to point of differentiation. The necessary conditions of optimality fot the nonlinear infinite dimensional systems without differentiability of system state to the control are accepted. The conception of the sequential model and sequential state for the mathematical physic problems are proposed. It is indicate, that the creation of mathematical model, quality analysis of the system and basing of numerical method of resolution are realized together with use of sequential method. It is exhibited the binding of sequential state and rhe generalized resolution of the mathematicsl physics problem. The sequential extention of optimal control problem is proposed.
Main publications:
Serovajsky S. Arithmetical Distributions and the Sequential Extension of Binary Relations // Mathematical notes, v. 65, no. 6, 1999, 705–717.
