ABSTRACT
This chapter presents statements of problems rather than the exposition of the results. It explains the perturbations of simple "model" systems of equations and the construction of a discrete analog of jet bundles used in the general theory of solvability of partial differential equations. The chapter shows that despite its significance and the variety of applications, the perturbation theory for operators in partial derivatives in a hardly satisfactory state except for its special divisions. It describes the process of the search for an answer to the question: "To what extent differential operators can use a discrete object for simulating certain concepts used in the general theory of solvability of partial differential equations?" The indicated concepts include jet bundles and elements of the homology theory. The suggested structural analysis of simple models that refer to the influence exerted by the perturbations of a domain on the spectrum of the operator defined in it may prove to be useful.
