Unilateral global bifurcation for an overdetermined problem in SN × R and HN × R
We establish the Dancer-type unilateral global bifurcation theorem for nonlinear operator equation of u + f(λ, u) = F(λ, u) = 0, where X is a real Banach space and f : R × X → X is completely continuous with f(λ, 0) = 0 and C 1 with respect to u at u = 0. We shall show that, if dimKer(DuF(µ, 0)) = 1...
Elmentve itt :
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| Dokumentumtípus: | Folyóirat |
| Megjelent: |
2025
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| Sorozat: | Electronic journal of qualitative theory of differential equations
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| Kulcsszavak: | Bifurkáció |
| Tárgyszavak: | |
| doi: | 10.14232/ejqtde.2025.1.48 |
| Online Access: | http://acta.bibl.u-szeged.hu/88928 |
| Tartalmi kivonat: | We establish the Dancer-type unilateral global bifurcation theorem for nonlinear operator equation of u + f(λ, u) = F(λ, u) = 0, where X is a real Banach space and f : R × X → X is completely continuous with f(λ, 0) = 0 and C 1 with respect to u at u = 0. We shall show that, if dimKer(DuF(µ, 0)) = 1 for some µ ∈ R and DuF(λ, 0) has an odd crossing number at λ = µ, there exist two branches C (ν ∈ {+, −}) emanating from (µ, 0), such that either C µ and C µ are both unbounded or C µ ∩ C µ ̸= {(µ, 0)}. As one of applications, we obtain the unilateral global bifurcation result for an overdetermined problem in SN × R and HN × R. |
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| Terjedelem/Fizikai jellemzők: | 10 |
| ISSN: | 1417-3875 |