Global Solutions of Nonlinear Problem in Hilbert Space

We deal with the local and global existence of solutions and solutions multiplicity for nonlinear problem u – λLu + N (u) = 0 in a real Hilbert space H, with linear operator L and nonlinear operator N, defined on a Hilbert space H, in dependence on a parameter λ ∈ R. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)