On the regularization of a matrix differential-algebraic boundary-value problem

Solvability conditions for nonlinear matrix equations

“…(3.7) and, hence, the original equation (1.1 ) cannot be solved, Eq. (3.7) can be regularized similarly to what was done in work [24].…”

Nonlinear Integrodifferential Boundary-Value Problems Unsolvable with Respect to the Derivative

“…( 10), we get the critical case and, moreover, condition (4) is satisfied. In addition, the generating boundary-value problem has a solution independent of an arbitrary continuous vector function ⌫ Note that, in the case where the nonlinear integrodifferential boundary-value problem (1), ( 2) is unsolvable, it can be regularized by analogy with [11,12]. We also note that the proposed scheme of investigation of the nonlinear integrodifferential boundary-value problem (1), ( 2) can be generalized to the case of integrodifferential boundary-value problems with delay [1,[13][14][15][16].…”

“…1 .t/: y 0 .t; c r / D X r .t /c r C GOEf .s/I 0ç.t /; c r 2 R The required periodic solution of the boundary-value problem (12)y.t/ D y 0 .t; c r / C x.t/; x.t/ D X.t /v C ‰.t /u; u.c 0 / D P 0 c 0 ; v.c 1 / D P 1 c 1for the nonlinear integrodifferential boundary-value problem (1), (2) unsolved with respect to the derivative is determined by the vector L c satisfying the nonlinear equation (7); here, and moreover, the condition of solvability (11) is satisfied. Thus, we get the one-parameter periodic solution of the nonlinear integrodifferential boundary-value problem(12) …”