Nonlinear integrodifferential boundary value problems with deviating argument unsolved with respect to the derivative - Boichuk, O. A.; Chuiko, S. M.; Kuzmina, V. O. (Ukrains’kyi Matematychnyi Zhurnal, 2022)
UDC 517.9 The investigations of linear differential-algebraic boundary-value problems are closely connected with numerous applications of the corresponding mathematical models in the theory of nonlinear oscillations, mechanics, biology, radio-engineering, and the theory of stability of motion. Thus, the problem of generalization of the results obtained by S. Campbell, A. M. Samoilenko and O. A. Boichuk to the case of nonlinear boundary-value problems unsolved with respect to the derivative seems to be quite urgent. In particular, this is true for finding necessary and sufficient conditions for the existence of the required solutions of nonlinear integrodifferential boundary-value problems with deviating argument unsolved with respect to the derivative. We establish the conditions for existence and propose a constructive scheme for finding the solutions of a nonlinear integrodifferential boundary-value problem with deviating argument unsolved with respect to the derivative.