Work

Modern science common necessity is a need to develop constructive methods for the study of boundary value problems for operator-differential and evolution equations. Such problems model many physical, technical, economic, and social processes. For the analysis of linear and nonlinear boundary value problems for a wide class of differential, integral, function-differential, integro-differential systems, systems and equations with delay and momentum their development occupies one of the central places within the field of Qualitative theory of differential equations. An important aspect of the theory of boundary value problems for operator-differential and evolution equations is the study of the solvability of such problems with conditions at infinity. Such boundary value problems were previously investigated in the case when the linearized part of the corresponding operators was Fredholm or Fredholm with zero index. Therefore, the study of operator-differential boundary value problems, the linearized part of which is a normal-solvable or generalized normal-solvable operator is a topical issue that requires detailed study. It should be noted that the minimal discrete s-energy has a large number of applications. One example of such applications is the "Thomson problem" (about the minimization of the potential energy of discrete charge systems) and the generalization of this problem, which use the Riesz s-potential. Despite the fact that a large number of works are devoted to the asymptotic decomposition of the Riesz minimum energy, finding the value of the coefficient of the second term is still an important and complex unsolved problem.