Bifurcation for Semi-linear Elliptic Problems on an Infinite Strip Via the Nash-Moser Technique

Abstract

The one-sided local bifurcation of decaying solutions (solitary waves) for a semi-linear elliptic boundary-value problem is established with an assumption of non-degeneracy. The Nash-Moser technique is used to overcome certain difficulties associated with the unboundedness of the domain and the long wavelength of the solution. The results of Kirchgdssner are thereby strengthened slightly.