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 sublinear with respect to the variable z at infinity. We study the existence of solutions when a double resonance phenomenon occurs by the introduction of Landesman–Lazer type conditions. Applications to scalar second order differential equations are given.
Double resonance in sturm–liouville planar boundary value problems / Sfecci, A.. - In: TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS. - ISSN 1230-3429. - STAMPA. - 55:2(2020), pp. 655-680. [10.12775/TMNA.2019.109]
Double resonance in sturm–liouville planar boundary value problems
Sfecci A.
2020-01-01
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 sublinear with respect to the variable z at infinity. We study the existence of solutions when a double resonance phenomenon occurs by the introduction of Landesman–Lazer type conditions. Applications to scalar second order differential equations are given.| File | Dimensione | Formato | |
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