Multiplicity results for superquadratic Dirichlet boundary value problems in $\mathbb R^2$

Abstract

In this paper it is studied the Dirichlet problem associated to the planar system $z'=J\nabla F(t,z)$. We consider the situation where the Hamiltonian $F$ satisfies a superquadratic-type condition at infinity.

By means of a bifurcation argument we prove the existence of infinitely many solutions. These solutions are distinguished by the Maslov index of an associated linear system.