Homotopy perturbation method for nonlinear oscillators with coordinate-dependent mass

Nonlinear oscillators with no linear term or negative linear term are difficult to be solved analytically. This paper shows that the homotopy perturbation method can be effectively applied to such kinds of nonlinear oscillator by the parameter expansion technology. A nonlinear oscillator with coordinate-dependent mass is used as an example to elucidate the effectiveness and convenience of the method. The condition for periodic solution is obtained.