In the present study, some perturbation methods are applied to Duffing equations having a displacement time-delayed variable to study the stability of such systems. Two approaches are considered to analyze Duffing oscillator having a strong delayed variable. The homotopy perturbation method is applied through the frequency analysis and nonlinear frequency is formulated as a function of all the ...

In this paper, we investigate a singular perturbation problem including a fourth order O.D.E. with general linear boundary conditions. Firstly, we obtain the necessary conditions of solution of O.D.E. by making use of fundamental solution, then by compatibility of these conditions with boundary conditions, we determine that, for given perturbation problem, whether boundary layer is formed or not.

in this paper, we investigate a singular perturbation problem including a fourth order o.d.e. with general linear boundary conditions. firstly, we obtain the necessary conditions of solution of o.d.e. by making use of fundamental solution, then by compatibility of these conditions with boundary conditions, we determine that, for given perturbation problem, whether boundary layer is formed or not.

singular perturbation problems have been studied by many mathematicians. since the approximate solutions of these problems are as the sum of internal solution (boundary layer area) and external ones, the formation or non-formation of boundary layers should be specified. this paper, investigates this issue for a singular perturbation problem including a first order differential equation with gen...

We study the parity breaking effective action in 2 + 1 dimensions, generated, at finite temperature, by massive fermions interacting with a non-Abelian gauge background. We explicitly calculate, in the static limit, parity violating amplitudes up to the seven point function, which allows us to determine the corresponding effective actions. We derive the exact parity violating effective action w...

We study the parity breaking effective action in 2 + 1 dimensions, generated, at finite temperature, by massive fermions interacting with a non-Abelian gauge background. We explicitly calculate, in the static limit, parity violating amplitudes up to the seven point function, which allows us to determine the corresponding effective actions. There are two classes of such actions that arise, namel...