A global bifurcation theorem with applications to nonlinear Picard problems (Q1582107)

The authors generalize the known \textit{P. H. Rabinowitz} [J. Funct. Anal. 7, 487-513 (1971; Zbl 0212.16504)] result about the existence of a closed and connected set of nontrivial solutions for the nonlinear eigenvalue problem \(f(\lambda,x)\equiv x-F(\lambda,x)=0\) with a completely continuous map \(F:R\times E\rightarrow E\) not necessarily differentiable at \(O\). The application to the nonlinear Picard problem \[ u''(t)+p(\lambda,t,u(t),u'(t))=0, \quad u(0)=u(\pi)=0 \] with the right side given by the Carathéodory function is considered.