A global bifurcation theorem for a multiparameter positone problem and its application to the one-dimensional perturbed Gelfand problem
We 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 h...
Elmentve itt :
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| Dokumentumtípus: | Folyóirat |
| Megjelent: |
2019
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| Sorozat: | Electronic journal of qualitative theory of differential equations
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| Kulcsszavak: | Gelfand probléma, Bifurkáció |
| doi: | 10.14232/ejqtde.2019.1.99 |
| Online Access: | http://acta.bibl.u-szeged.hu/66366 |
| Tartalmi kivonat: | We 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. |
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| Terjedelem/Fizikai jellemzők: | 1-25 |
| ISSN: | 1417-3875 |