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.
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 in questo prodotto:
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Rev2_TMNA.pdf
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