# Resonant Sturm–Liouville Boundary Value Problems for Differential Systems in the Plane

@inproceedings{Boscaggin2016ResonantSB, title={Resonant Sturm–Liouville Boundary Value Problems for Differential Systems in the Plane}, author={Alberto Boscaggin and Maurizio Garrione}, year={2016} }

We study the Sturm-Liouville boundary value problem associated with the planar differential system Jz′ = ∇V (z) + R(t, z), where V (z) is positive and positively 2-homogeneous and R(t, z) is bounded. Assuming Landesman-Lazer type conditions, we obtain the existence of a solution in the resonant case. The proofs are performed via a shooting argument. Some applications to boundary value problems associated with scalar second order asymmetric equations are discussed. MSC 2010 Classification 34B15.

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## Double resonance in Sturm-Liouville planar boundary value problems.

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