Document Type
Article
Department
Mathematics (HMC)
Publication Date
1993
Abstract
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.
Rights Information
© 1993 Dynamic Publishers
Recommended Citation
Castro, Alfonso and Jorge Cossio. “A bifurcation theorem and applications”, Dynamic Systems and Applications, Vol. 2 (1993), pp. 221-226.
Included in
Mathematics Commons, Ordinary Differential Equations and Applied Dynamics Commons, Partial Differential Equations Commons
