We consider bifurcation from the trivial branch for nondifferentiable perturbations of linear operators with compact resolvent. Comparing the growth of the nonlinearity at 0 with the norm of the resolvent for values of μ close to an eigenvalue μ 0 of the operator with odd multiplicity, conditions are obtained ensuring that some neighborhood of μ 0 contains a bifurcation point.
Chiappinelli, R. (1989). Remarks on Krasnoselʹskiĭ bifurcation theorem. COMMENTATIONES MATHEMATICAE UNIVERSITATIS CAROLINAE, 30(2), 235-241.
Remarks on Krasnoselʹskiĭ bifurcation theorem
CHIAPPINELLI, RAFFAELE
1989-01-01
Abstract
We consider bifurcation from the trivial branch for nondifferentiable perturbations of linear operators with compact resolvent. Comparing the growth of the nonlinearity at 0 with the norm of the resolvent for values of μ close to an eigenvalue μ 0 of the operator with odd multiplicity, conditions are obtained ensuring that some neighborhood of μ 0 contains a bifurcation point.
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https://hdl.handle.net/11365/32311
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