Basic topological structures of the theory of ordinary differential equations
We consider a fourth order eigenvalue problem containing a spectral parameter both in the equation and in the boundary condition. The oscillation properties of eigenfunctions are studied and asymptotic formulae for eigenvalues and eigenfunctions are deduced. The basis properties in L p(0; l); p ∈ (1;∞); of the system of eigenfunctions are investigated.
The modified generalized Van der Pol-Mathieu equation is generalization of the equation that is investigated by authors Momeni et al. (2007), Veerman and Verhulst (2009) and Kadeřábek (2012). In this article the Bautin bifurcation of the autonomous system associated with the modified generalized Van der Pol-Mathieu equation has been proved. The existence of limit cycles is studied and the Lyapunov quantities of the autonomous system associated with the modified Van der Pol-Mathieu equation are computed....
This contribution is devoted to the problem of asymptotic behaviour of solutions of scalar linear differential equation with variable bounded delay of the form with positive function Results concerning the structure of its solutions are obtained with the aid of properties of solutions of auxiliary homogeneous equation where the function is positive. A result concerning the behaviour of solutions of Eq. (*) in critical case is given and, moreover, an analogy with behaviour of solutions of...