On the existence of solutions for strongly nonlinear differential equations (Q929600)

The objective of this paper is to find approximate solutions to the differential equation \[ \ddot{x}(t)+a{\dot{x}}^2(t)+bx(t)=F(t). \] The authors prove that if \(F\) is a bounded, odd periodic function, then under suitable conditions on it and its derivative, there exists a solution in the mean of the differential equation which is computable. The paper contains also a discussion on the homotopy perturbation method applied to the construction of analytic solutions of the differential equation but it does not contain results on the converge of the method.