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

Alberto Boscaggin | Zendy; Maurizio Garrione | Zendy

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

Author(s) -

Alberto Boscaggin,

Maurizio Garrione

Publication year - 2015

Publication title -

zeitschrift für analysis und ihre anwendungen

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.567

H-Index - 35

eISSN - 1661-4534

pISSN - 0232-2064

DOI - 10.4171/zaa/1554

Subject(s) - sturm–liouville theory , boundary value problem , plane (geometry) , value (mathematics) , mathematical analysis , differential (mechanical device) , mathematics , physics , geometry , statistics , thermodynamics

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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