Asymptotically linear Hamiltonian systems with Lagrangian boundary conditions
Let us consider the nonlinear Hamiltonian system \(\frac{dx}{dt}=JH'(t,x(t))\) where \(x(t)\in \mathbb{R}^{2n}\) and \(J\) is the standard symplectic matrix. For a fixed \(L\in \Lambda (n)\)=the set of all Lagrangian subspaces of \(\mathbb{R}^{2n}\) the Lagrangian boundary conditions \(x(0)\in L, x(1)\in L\) are added. Then, the multiplicity of solutions for the above Hamiltonian system with the supplementary hypothesis of asymptotically linearity are studied using a Maslov type theory.
scientific article; zbMATH DE number 5366262