Bifurcation for second-order Hamiltonian systems with periodic boundary conditions
Summary: Through variational methods, we study nonautonomous systems of second-order ordinary differential equations with periodic boundary conditions. First, we deal with a nonlinear system, depending on a function \(u\), and prove that the set of bifurcation points for the solutions of the system is not \(\sigma \)-compact. Then, we deal with a linear system depending on a real parameter \(\lambda >0\) and on a function \(u\), and prove that there exists \(\lambda ^{\ast }\) such that the set of the functions \(u\), such that the system admits nontrivial solutions, contains an accumulation point.
second-order ordinary differential equations
scientific article; zbMATH DE number 5313165
scientific article