In this paper, we study a class of nonlinear Duffing equations with a deviating argument and establish some sufficient conditions for the existence of positive almost periodic solutions of the equation. These conditions are new and complement to previously known results.

In recent years, many authors are greatly attached to investigation for the existence and uniqueness of solution of Duffing equations, for example, 1–11 , and so forth. Some authors 8, 11, 12 , etc. proved the existence and uniqueness of solution of Duffing equations underC2 perturbation functions and other conditions at nonresonance by employingminimax theorems. In 1986, Tersian investigated t...

In this paper, we analyze the damped Duffing equation by means of qualitative theory of planar systems. Under certain parametric choices, the global structure in the Poincaré phase plane of an equivalent two-dimensional autonomous system is plotted. Exact solutions are obtained by using the Lie symmetry and the coordinate transformation method, respectively. Applications of the second approach ...

We propose a mean-field approach to the Duffing oscillator to construct perturbatively the bounded operators that generate the quantum states, and to define a non-Gaussian density operator. 1 The Duffing oscillator is a typical anharmonic oscillator whose classical aspect is relatively well-understood [1]. It has been studied in many fields of physics from classical mechanics to quantum mechani...

In this paper, we study the traveling wave solutions of fractional generalized reaction Duffing equation, which contains several nonlinear conformable time equations. By dynamic system method, phase portraits equation are given, and all possible exact obtained.

In this paper, we study the following Duffing-type equation: x′′ + cx′ + g(t, x) = h(t), where g(t, x) is a 2π-periodic continuous function in t and concave-convex in x, and h(t) is a small continuous 2π-periodic function. The exact multiplicity and stability of periodic solutions are obtained.