The Lower Bounds of T-Periodic Solutions for the Forced Duffing Equation

Abstract

This paper is devoted to the discussion of the number of T -periodic solutions for the forced Duffing equation, x + kx + g t x = s 1 + h t , with g t x being a continuous function by using the degree theory, upper and lower solutions method, and the twisting theorem.

A pseudospectral method for nonlinear Duffing equation involving both integral and non‐integral forcing terms

“…This equation is used to discuss some important practical phenomena such as orbit extraction, nonuniformity caused by an infinite domain, nonlinear mechanical oscillators, and prediction of diseases. [3][4][5][6][7][8]. In this paper, we consider the following Duffing equation involving both integral and non-integral forcing terms y 00 .x/ C y 0 .x/ C f .x, y.x/, y 0 .x// C…”

Numerical solutions of Duffing equations involving both integral and non-integral forcing terms

“…[1][2][3][4][5]. In [6,7], the quasilinearization technique was applied to obtain the analytic approximations of the solutions of forced Duffing equations with continuous and noncontinuous integral boundary conditions.…”

Solving the forced Duffing equation with integral boundary conditions in the reproducing kernel space

“…It is well known that the forced Duffing equation arises in a variety of different scientific fields such as periodic orbit extraction, nonuniformity caused by an infinite domain, nonlinear mechanical oscillators, prediction of diseases, etc. [2,4,16,30,32]. The numerical solutions of the forced Duffing equation with two-point boundary conditions have been investigated by many researchers [23,24,26,27,31].…”