This paper provides supplementary information on the Krasnoselʹskiĭ bifurcation theorem for gradient mappings ∇φ(u)=λu in a real Hilbert space. Strengthening the differentiability assumption, we prove a better estimate of the form λ r =λ 0 +O(r p−1 ) for the bifurcating solutions (u r ,λ r ) on the sphere S r . Applications are given to nonlinear elliptic eigenvalue problems of the form −Δu=μ(u+f(x,u)), x∈Ω, u=0, x∈∂Ω .
Chiappinelli, R. (1997). An estimate on the eigenvalues in bifurcation for gradient mappings. GLASGOW MATHEMATICAL JOURNAL, 39(2), 211-216.
An estimate on the eigenvalues in bifurcation for gradient mappings
CHIAPPINELLI, RAFFAELE
1997-01-01
Abstract
This paper provides supplementary information on the Krasnoselʹskiĭ bifurcation theorem for gradient mappings ∇φ(u)=λu in a real Hilbert space. Strengthening the differentiability assumption, we prove a better estimate of the form λ r =λ 0 +O(r p−1 ) for the bifurcating solutions (u r ,λ r ) on the sphere S r . Applications are given to nonlinear elliptic eigenvalue problems of the form −Δu=μ(u+f(x,u)), x∈Ω, u=0, x∈∂Ω .I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
https://hdl.handle.net/11365/32045
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