Bifurcation problems for equations involving Lipschitz continuous mappings (Q809242)

Let X,Y be Banach spaces, \(\Lambda\) an open subset in a normed space, \(\bar D\) a closed 0-neighborhood in X, \(v\mapsto T(v)\), and \(v\mapsto L(\lambda,v)\) continuous linear operators from X into Y for any \(\lambda \in \Lambda\), and H,K: \(\Lambda \times \bar D\to Y\) continuous nonlinear operators. The author solves the bifurcation problem \[ T(v)=L(\lambda,v)+H(\lambda,v)+K(\lambda,v),\quad (\lambda,v)\in \Lambda \times \bar D, \] where the operators L,H are positive homogeneous in \(\lambda\), and H,K Lipschitz continuous. The paper generalizes older results by the author.