Gruendler, Joseph Homoclinic solutions for autonomous ordinary differential equations with nonautonomous perturbations. (English) Zbl 0840.34045 J. Differ. Equations 122, No. 1, 1-26 (1995). 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. Reviewer: S.Yu.Pilyugin (St.Peterburg) Cited in 53 Documents MSC: 34C37 Homoclinic and heteroclinic solutions to ordinary differential equations 34C23 Bifurcation theory for ordinary differential equations 34D10 Perturbations of ordinary differential equations Keywords:Lyapunov-Schmidt method; bifurcation equation; homoclinic solutions × Cite Format Result Cite Review PDF Full Text: DOI