Korol' I. I.
Ukr. Mat. Zh. - 2008. - 60, № 3. - pp. 332–339
We analyze the conditions of existence and the numerical-analytic method for the approximate construction of periodic solutions of nonlinear autonomous systems of differential equations in the critical case.
Ukr. Mat. Zh. - 2006. - 58, № 4. - pp. 472–488
A new numerical-analytic algorithm for the investigation of periodic solutions of nonlinear periodic systems of differential equations dx/dt = A(t) x+ ƒ(t, x) in the critical case is developed. The problem of the existence of solutions and their approximate construction is studied. Estimates for the convergence of successive periodic approximations are obtained.
Ukr. Mat. Zh. - 2005. - 57, № 4. - pp. 483–495
We study the problem of the existence of periodic solutions of two-dimensional linear inhomogeneous periodic systems of differential equations for which the corresponding homogeneous system is Hamiltonian. We propose a new numerical-analytic algorithm for the investigation of the problem of the existence of periodic solutions of two-dimensional nonlinear differential systems with Hamiltonian linear part and their construction. The results obtained are generalized to systems of higher orders.
Ukr. Mat. Zh. - 1994. - 46, № 8. - pp. 1031–1042
We suggest a modification of the numerical-analytic iteration method. This method is used for studying the problem of existence of solutions and for constructing approximate solutions of nonlinear two-point boundary-value problems for ordinary differential equations with unknown parameters both in the equation and in boundary conditions.