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Zeitschrift für Analysis und ihre Anwendungen


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Volume 35, Issue 1, 2016, pp. 41–59
DOI: 10.4171/ZAA/1554

Published online: 2015-12-23

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

Alberto Boscaggin[1] and Maurizio Garrione[2]

(1) Università di Torino, Italy
(2) Università di Milano-Bicocca, Italy

We study the Sturm-Liouville boundary value problem associated with the planar differential system $Jz'=\nabla V(z) + R(t, z)$, 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.

Keywords: Positively homogeneous systems, Sturm–Liouville boundary value problems, resonance, Landesman–Lazer conditions

Boscaggin Alberto, Garrione Maurizio: Resonant Sturm–Liouville Boundary Value Problems for Differential Systems in the Plane. Z. Anal. Anwend. 35 (2016), 41-59. doi: 10.4171/ZAA/1554