Couples of lower and upper slopes and resonant second order ordinary differential equations with nonlocal boundary conditions
(2016) Mathematica Bohemica — Vol. 141, n° 2, p. 239-259 (2016)
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- A couple (σ, τ) of lower and upper slopes for the resonant second order boundary value problem (formula present), with g increasing on [0, 1] such that (formula present), is a couple of functions σ, τ ϵ C1([0, 1]) such that σ(t) τ ≤ (t) for all t ϵ [0, 1], (formula present), in the stripe (formula present) and t ϵ [0, 1]. It is proved that the existence of such a couple (σ, τ) implies the existence and localization of a solution to the boundary value problem. Multiplicity results are also obtained.
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Mawhin, J., & Szymańska-Dębowska, K. (2016). Couples of lower and upper slopes and resonant second order ordinary differential equations with nonlocal boundary conditions. Mathematica Bohemica, 141(2), 239-259. https://doi.org/10.21136/mb.2016.17 (Original work published 2016)