Double resonance in Sturm-Liouville planar boundary value problems

Andrea Sfecci

Abstract


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.

Keywords


Positively homogeneous planar systems; Sturm-Liouville boundary value problems; Dirichlet problem; shooting method; double resonance; Landesman-Lazer conditions

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