SZTE Repository of Papers and Books: No conditions. Results ordered -Date Deposited. 2021-01-22T04:34:41ZEPrintshttp://acta.bibl.u-szeged.hu/images/acta.jpghttp://acta.bibl.u-szeged.hu/2020-01-28T09:35:20Z2020-07-29T12:24:56Zhttp://acta.bibl.u-szeged.hu/id/eprint/66366This item is in the repository with the URL: http://acta.bibl.u-szeged.hu/id/eprint/663662020-01-28T09:35:20ZA global bifurcation theorem for a multiparameter positone problem and its application to the one-dimensional perturbed Gelfand problemWe study the global bifurcation and exact multiplicity of positive solutions for u 00(x) + λ fε(u) = 0, − 1 < x < 1, u(−1) = u(1) = 0, where λ > 0 is a bifurcation parameter, ε ∈ Θ is an evolution parameter, and Θ ≡ (σ1, σ2) is an open interval with 0 ≤ σ1 < σ2 ≤ ∞. Under some suitable hypotheses on fε , we prove that there exists ε0 ∈ Θ such that, on the (λ, kuk∞)-plane, the bifurcation curve is S-shaped for σ1 < ε < ε0 and is monotone increasing for ε0 ≤ ε < σ2. We give an application to prove global bifurcation of bifurcation curves for the one-dimensional perturbed Gelfand problem.Shao-Yuan HuangKuo-Chih HungShin-Hwa Wang