BOUNDARY PROBLEM WITH IMPULSE ACTION (SECOND ORDER CRITICAL CASE)
Journal Title: Енергетика і автоматика - Year 2018, Vol 0, Issue 6
Abstract
It is shown that the existence of an initial boundary value problem depends on the condition, compiled with the help of nonlinearity and the first approximation to the desired solution. We find the necessary and sufficient conditions for the existence of a solution of the boundary value problem with a pulsed action, which is a second approximation to the desired one. Conditions were studied in the case of failure to fulfill the desired solution of the considered boundary value problem with pulsed action, which is determined by the method of simple iterations, doesn’t exist. Conditions for the construction of a boundary value problem with a pulsed action to the operator system are found, which is sufficient to prove the existence of the solution of such boundary value problem. The theorem is formulated, which allows us to find a single solution, which is determined by the iterative process. Effective methods of perturbation theory are used, developed in the works of M. Krylov, M. Bogolyubov, Y. Mitropolsky, A. Samoilenko. New results are obtained, which complement research in the theory of nonlinear oscillations for boundary value problems with impulse action.
Authors and Affiliations
Р. Ф. ОВЧАР
Keywords
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BOUNDARY PROBLEM WITH IMPULSE ACTION (SECOND ORDER CRITICAL CASE)
It is shown that the existence of an initial boundary value problem depends on the condition, compiled with the help of nonlinearity and the first approximation to the desired solution. We find the necessary and sufficie...