Approximate solutions of the forced Duffing equation with mixed nonlinearities.
Approximation of periodic solutions of a system of periodic linear nonhomogeneous differential equations
The present paper does not introduce a new approximation but it modifies a certain known method. This method for obtaining a periodic approximation of a periodic solution of a linear nonhomogeneous differential equation with periodic coefficients and periodic right-hand side is used in technical practice. However, the conditions ensuring the existence of a periodic solution may be violated and therefore the purpose of this paper is to modify the method in order that these conditions remain valid....
Approximative sequences and almost homoclinic solutions for a class of second order perturbed Hamiltonian systems
In this work we will consider a class of second order perturbed Hamiltonian systems of the form , where t ∈ ℝ, q ∈ ℝⁿ, with a superquadratic growth condition on a time periodic potential V: ℝ × ℝⁿ → ℝ and a small aperiodic forcing term f: ℝ → ℝⁿ. To get an almost homoclinic solution we approximate the original system by time periodic ones with larger and larger time periods. These approximative systems admit periodic solutions, and an almost homoclinic solution for the original system is obtained...
Asymptotic behavior of non-linear inhomogeneous differential equations via non-standard analysis. Part II. Some applications to higher order equations
Asymptotic behavior of -periodic solutions of singularly perturbed second-order differential equation
Asymptotic conditions for solving non-symmetric problems of third order nonlinear differential systems.
Asymptotic properties of mild solutions of nonautonomous evolution equations with applications to retarded differential equations.
Averaging in an ordinary differential equation.