On the Solvability of a Periodic Problem for Nonlinear Ordinary Differential Equation of the Second Order

In this paper is investigated the solvability of a periodic problem for a system of nonlinear ordinary differential equations second order with the main positively homogeneous part. New conditions have been found that provide an a priori estimate solutions of the periodic problem under consideration. The conditions for the a priori estimate are formulated in terms of the properties of the main positively homogeneous part of the system of equations. Under the conditions of an a priori estimate, using and developing methods for calculating the mapping degree, a theorem on the solvability of the periodic problem is proven. The proven theorem generalizes previously obtained the authors’ results on the study of a periodic problem for systems of nonlinear ordinary differential equations of the second order.

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On the Solvability of a Periodic Problem for Nonlinear Ordinary Differential Equation of the Second Order

Cited by 3 publications

References 1 publication

On the Solvability of a Periodic Problem for a System of Second-Order Nonlinear Ordinary Differential Equations

On the Solvability of a Periodic Problem for a System of Second-Order Nonlinear Ordinary Differential Equations

On a Priori Estimation of Periodic Solutions to a System of Nonlinear Ordinary Differential Equations of the Second Order

On the Solvability of a Periodic Problem for a System of Nonlinear Ordinary Differential Equations of the Second Order

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