This paper studies the problem of the continuous dependence of Van der Pol equation solutions with respect to the boundary conditions. We provide a new approach for the existence of such solutions via p-regularity theory. Several existence theorems about continuous solutions are established.

The paper studies the existence problem of periodic solutions of the nonlinear dynamical systems in the singular case. We prove a certain generalization of the Andronov-Hopf theorem. This generalization is based on an application of the theorem on a modified p-factor operator. It also uses some other results and constructions of the p-regularity theory. Moreover, we prove theorems on the solution's uniqueness. We illustrate our results by the example of a nonlinear dynamical system of ordinary differential equations. Our purpose is to find periodic solutions of such system with fixed period 2π . This is a new research in relation to previous work, where the authors were looking for periodic solutions with period near 2π .

The paper studies a solution existence problem of the nonlinear Duffing equation of the formwhere] and x(0) = x(2π ) = 0 using the p-regularity theory.

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