Bifurcation from characteristic values of arbitrary multiplicity

Existence theorems are proved for bifurcation points of the system F(λ,x)εC, where C is a closed cone in a Banach space. A parameter family of nontrivial solutions in a neighborhood of a bifurcation point are described in an analytic form. Different forms of linearization are utilized, which are weaker than continuous Frechet differentiability. The multiplicity of the characteristic value of the linearized part is not restricted. A principal tool is the use of generalized implicit function theorems for operators whose derivative has no bounded inverse or whose range is not necessarily closed. Existence of bifurcation points is established for a class of operator equations of the form T = l(7lambda;,v)+H(λ,v)+K(λ,v), where T and L(λ,.) are linear (not necessarily bounded) mappings, and H, K are nonlinear mappings that satisfy certain assumptions.