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 sublinear with respect to the variable z at infinity. We study the existence of solutions when a double resonance phenomenon occurs by the introduction of Landesman–Lazer type conditions. Applications to scalar second order differential equations are given.
