Multiple homoclinic solutions for singular differential equations
Annales de l'I.H.P. Analyse non linéaire, Volume 27 (2010) no. 3, p. 917-936

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.

DOI : https://doi.org/10.1016/j.anihpc.2010.01.005
Keywords: Degenerate homoclinic solution, Lyapunov–Schmidt reduction, Singular perturbations, Codimension
@article{AIHPC_2010__27_3_917_0,
author = {Zhu, Changrong and Luo, Guangping and Lan, Kunquan},
title = {Multiple homoclinic solutions for singular differential equations},
journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
publisher = {Elsevier},
volume = {27},
number = {3},
year = {2010},
pages = {917-936},
doi = {10.1016/j.anihpc.2010.01.005},
zbl = {1217.34075},
mrnumber = {2629886},
language = {en},
url = {http://www.numdam.org/item/AIHPC_2010__27_3_917_0}
}

Zhu, Changrong; Luo, Guangping; Lan, Kunquan. Multiple homoclinic solutions for singular differential equations. Annales de l'I.H.P. Analyse non linéaire, Volume 27 (2010) no. 3, pp. 917-936. doi : 10.1016/j.anihpc.2010.01.005. http://www.numdam.org/item/AIHPC_2010__27_3_917_0/

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