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arXiv · 1810.10210

Double resonance in Sturm-Liouville planar boundary value problems

Andrea Sfecci
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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 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.

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Andrea Sfecci. 2018-10-24. Double resonance in Sturm-Liouville planar boundary value problems. https://doi.org/10.12775/tmna.2019.109

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