Periodic solutions of some classes of continuous second-order differential equations (Q524006)

The authors study the periodic problem associated to the following differential equations: \[ x''\pm x^n=\mu f(t),\qquad x''\pm |x|^n=\mu f(t), \] where \(f(t)\) is a continuous \(T\)-periodic function with \(\int_0^Tf(t)dt\neq0\), \(n\geq4\) is an integer, and \(\mu>0\) is a small parameter. They prove the existence of at least two \(T\)-periodic solutions, and determine some stability properties of these.