  We provide some existence results for Sturm-Liouville boundary value problems
associated with the planar differential system $Jz' = g(t, z) + r(t, z)$ where
g is suitably controlled by the gradient of two positively homogeneous
functions of degree 2 and r is bounded. We study the existence of solutions
when a double resonance phenomenon occurs by the introduction of
Landesman-Lazer type of conditions. Applications to scalar second order
differential equations are given.
