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

DOI: http://dx.doi.org/10.12775/TMNA.2008.002

#### 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.

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.

#### Keywords

Maslov index; bifurcation; boundary value problems

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