The stability of periodic solutions of non-linear differential equations with periodic coefficients has been of interest in mathematical physics for many years. The goal of this work is to continue our investigations to stability properties of some fundamental periodic solutions of strongly non-linear coupled Hill’s equations. c achieve this goal, we first solve analytically the differential equations using modified version of the generalized averaging method which has been developed for strongly non-linear problems. We test the validity of these approximate solutions numerically and a good agreement is found for large values of the coefficient of nonlinearity. A transformation is used to write our equations in the form which we can use the multiple-scaling technique. The stability analysis of solutions are studied as on example, and a good agreement is found between the analytical and numerical results.

Systems of nonlinear dierential equations with periodic coecients, which include Hill’s and Mathieu’s equations as examples in the linear limit, are important from a practical point of view. Nonlinear Hill’s equations model a variety of dynamical systems of interest to physics and engineering, in which perturbations enter as periodic modulations of their linear frequencies. As is well known, the stability properties of some fundamental periodic solutions of these systems is often an essential problem. The main purpose of this paper is to concentrate on one such class of nonlinear Hill’s equations and study the stability properties of some of their simplest periodic solutions analytically as well as numerically. To accomplish this task, we rst use an extension of the generalized averaging method to approximate these solutions and then apply the technique of multiple scaling to perform the stability analysis. A three-particle system with free–free boundary conditions is studied as an example. The accuracy of our results is tested, within the limits of rst-order perturbation theory, and is found to be well conrmed by numerical experiments. The stability analysis of these simple periodic solutions, though local in itself, can yield considerable information about more global properties of the dynamics, since it is in the vicinity of such solutions that the largest regions of regular or chaotic motion are usually observed, depending on whether the periodic solution is, respectively, stable or unstable.

This paper is concerned with the study of a class of variational inequalities with multivalued D

The purpose of this work is to establish the weak convergence results of the generalized Mann iterates for finding coincidence points of two self maps satisfying certain conditions in Banach spaces. An application of our results to the approximation of a solution of certain nonlinear operator equation with pseudomonotone operator is also given. Such problems arise in the description of steady state filtration processes. The results generalizes the corresponding theorems in [12].

We study some sets related to ij-delta open sets. Also, we study some separation axioms in bitopological spaces based on ij-deltaopen sets.