A Hamiltonian system with an even term
The author considers a Hamiltonian system of the form (1) \(u''+u= h(t)V(u)\), where \(h\) and \(V\) are differentiable, \(h>0\) and bounded, \(h(-t)=h(t)\), and \(V\) is a ``superquadratic'' potential. Under some natural additional conditions on \(h\) and \(V\), the author proves the existence of a non-zero solution \(w\) of (1), such that \(w'(0)= 0\) and \(w(t)\to 0\), \(w'(t)\to 0\) as \(t\to\infty\), using variational methods.
scientific article; zbMATH DE number 1157136