The homoclinic bifurcations of ordinary differential equation under singular perturbations are considered. We use exponential dichotomy, Fredholm alternative and scales of Banach spaces to obtain various bifurcation manifolds with finite codimension in an appropriate infinite-dimensional space. When the perturbative term is taken from these bifurcation manifolds, the perturbed system has various coexistence of homoclinic solutions which are linearly independent.
Cite this article
Guangping Luo, Kunquan Lan, Changrong Zhu, Multiple homoclinic solutions for singular differential equations. Ann. Inst. H. Poincaré Anal. Non Linéaire 27 (2010), no. 3, pp. 917–936DOI 10.1016/J.ANIHPC.2010.01.005