On the existence of solutions for strongly nonlinear differential equations
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.
scientific article; zbMATH DE number 5289218