In this paper we give a sufficient condition on the nonlinear operator N for a point (λ, u) to be a local bifurcation point of equations of the form u + λL-1(N(u)) = 0, where L is a linear operator in a real Hilbert space, L has compact inverse, and λ ∈ R is a parameter. Our result does not depend on the variational structure of the equation or the multiplicity of the eigenvalue of the linear operator L. Applications are made to systems of differential equations and to the existence of periodic solutions of nonlinear second order elliptic equations.
© 1993 Dynamic Publishers
Castro, Alfonso and Jorge Cossio. “A bifurcation theorem and applications”, Dynamic Systems and Applications, Vol. 2 (1993), pp. 221-226.