On bifurcation for nondifferentiable perturbations of selfadjoint operators. (English) Zbl 0581.47048

Ordinary and partial differential equations, Proc. 8th Conf., Dundee/Scotl. 1984, Lect. Notes Math. 1151, 109-114 (1985).
[For the entire collection see Zbl 0564.00005.]
Let H be a real Hilbert space and T: D(T)\(\to H\) a linear self-adjoint operator with discrete spectrum. It is shown that, if \(k>0\) and \(\lambda_ 0\) is an eigenvalue of T of odd multiplicity and isolation distance greater than 2k and \(F: H\to H\) satisfies \(\| F(u)\| \leq k\| u\|\) for all u in H, then global bifurcation of the problem \(Tu+F(u)=\lambda u\) takes place in the strip \([\lambda_ 0-k,\lambda_ 0+k]\times H\). Applications to ordinary differential equations are considered.
Reviewer: A.L.Andrew


47J05 Equations involving nonlinear operators (general)
34L99 Ordinary differential operators
34B15 Nonlinear boundary value problems for ordinary differential equations
47J10 Nonlinear spectral theory, nonlinear eigenvalue problems


Zbl 0564.00005