Two global several-parameter bifurcation theorems and their applications
This paper deals with the study of the nonlinear operator equation \[ u=L(\lambda)u+H(\lambda ,u),\quad u\in X, \] where \(X\) is a real Banach space, \(\lambda\in {\mathbb R}^m\), and \(L,H\) are continuous operators. The main result of this paper establishes a global bifurcation property, provided that \(L\) is a positively homogeneous completely continuous operator. In the case when \(L\) is a homogeneous completely continuous operator, it is established a unilateral global bifurcation result. A key role in the proofs is played by the Rabinowitz global bifurcation theorem in combination with topological degree arguments.
scientific article; zbMATH DE number 6487281