Global uniqueness of homoclinic orbits for a class of fourth order equations
There is a significant class of indefinite Hamiltonian systems for which there are strong and topologically robust theorems on the existence of orbits homoclinic to an equilibrium. In this paper the authors give sufficient conditions for uniqueness of these homoclinic orbits in \(\mathbb{R}^ 4\). Specifically they consider the equivalent equation \(\alpha x''''+\beta x''+\gamma x+k(x)=0\), \(x>0\), where \(\alpha,\gamma>0>\beta\), \(dk/dx<0\) for \(x>0\) and \(k(0)=0\). Uniqueness of homoclinic orbit is established using the maximal principle and some convexity arguments.
scientific article; zbMATH DE number 92527
scientific article