平面上微分系统的共振Sturm-Liouville边值问题

Pub Date : 2016-01-01 DOI:10.4171/ZAA/1554

A. Boscaggin, M. Garrione

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引用次数: 2

摘要

研究了平面微分系统Jz′=∇V (z) + R(t, z)的Sturm-Liouville边值问题，其中V (z)为正2齐次且R(t, z)有界。在Landesman-Lazer型条件下，我们得到了共振情况下解的存在性。证明是通过射击论证进行的。讨论了标量二阶非对称方程边值问题的一些应用。MSC 2010分类34B15。

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

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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