Subharmonic solutions of a nonconvex noncoercive Hamiltonian system
In this paper we study the existence of subharmonic solutions of the Hamiltonian system where u is a linear map, G is a C1-function and e is a continuous function.
In this paper we study the existence of subharmonic solutions of the Hamiltonian system where u is a linear map, G is a C1-function and e is a continuous function.
The generalized linear differential equation where and the matrices are regular, can be transformed using the notion of a logarithimc prolongation along an increasing function. This method enables to derive various results about generalized LDE from the well-known properties of ordinary LDE. As an example, the variational stability of the generalized LDE is investigated.
By using successive approximation, we prove existence and uniqueness result for a class of neutral functional stochastic differential equations in Hilbert spaces with non-Lipschitzian coefficients
Effective sufficient conditions for oscillation and nonoscillation of solutions of some operator-differential equations with piecewise constant argument are found.
In this paper, we consider polynomial systems of the form x' = y + P(x, y), y' = -x + Q(x, y), where P and Q are polynomials of degree n wihout linear part.For the case n = 3, we have found new sufficient conditions for a center at the origin, by proposing a first integral linear in certain coefficient of the system. The resulting first integral is in the general case of Darboux type.By induction, we have been able to generalize these results for polynomial systems of arbitrary degree.