Bifurcation of homoclinic solutions for Hamiltonian systems
Summary: We consider the Hamiltonian system \[ Ju'(x)+ Mu(x)- \nabla_uF\bigl(x,u(x) \bigr)=\lambda u(x). \] Using variational methods obtained by Stuart on the one hand and by Giacomoni and Jean-jean on the other, we get bifurcation results for homoclinic solutions by imposing conditions on the function \(F\). We study both the case where \(F\) is defined globally with respect to \(u\) and the case where \(F\) is defined locally only.
scientific article; zbMATH DE number 1925963