Homoclinic solutions for autonomous ordinary differential equations with nonautonomous perturbations (Q1900945)

Consider a system of the form \(x'= f_0(x)+ \mu_1 f_1(x, \mu, t)+ \mu_2 f_2(x, \mu, t)\), where \(x\in \mathbb{R}^n\), \(\mu= (\mu_1, \mu_2)\in \mathbb{R}^2\). It is assumed that for \(\mu= 0\) there exists a homoclinic trajectory. The author applies the Lyapunov-Schmidt method to construct a bifurcation equation \(H= 0\). This equation determines the bifurcation diagram for homoclinic solutions.