An extension of Krasnoselski theorem in local bifurcation theory

We give a local bifurcation result concerning the semilinear equation x = Lx+N(; x) in a Banach spaceX; self-adjoint where L is the linear self-adjoint operator and the nonlinearityN(;
) is compact, satisfying some boundedness conditions which are weaker than those from Krasnoselski theorem or than the usual uniform boundedness condition.