Unilateral Bifurcation for Several-Parameter Eigenvalue Problem with Homogeneous Operator

We establish the unilateral global bifurcation result for the following nonlinear operator equation u=L(λ)u+H(λ,u),(λ,u)∈Rm×X\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$u = L\left( \lambda \right)u + H\left( {\lambda,u} \right),\,\left( {\lambda,u} \right) \in \mathbb{R}{^m} \times X$$\end{document} where m is a positive integer, X is a Banach space, L(·) is a positively homogeneous completely continuous operator and H: ℝm·X → X is completely continuous with H = o (||u||) near u = 0 uniformly on bounded λ sets.