Weakly nonlinear boundary-value problem in a special critical case
We investigate the problem of the determination of conditions for the existence of solutions of weakly nonlinear Noetherian boundary-value problems for systems of ordinary differential equations and the construction of these solutions. We consider the special critical case where the equation for finding the generating solution of a weakly nonlinear Noetherian boundary-value problem turns into an identity. We improve the classification of critical cases and construct an iterative algorithm for finding solutions of weakly nonlinear Noetherian boundary-value problems in the special critical case.
English version (Springer): Ukrainian Mathematical Journal 61 (2009), no. 4, pp 657-673.
Citation Example: Chuiko S. M. Weakly nonlinear boundary-value problem in a special critical case // Ukr. Mat. Zh. - 2009. - 61, № 4. - pp. 548-562.