Kryszewski, Woyciech Some remarks on the continuation method in the fixed point theory. (English) Zbl 0776.47030 Zesz. Nauk. Wydz. Mat. Fiz. Chem., Mat., Gdańsk 6, 43-53 (1987). This article deals with some generalization of the classical continuation method in the theory of completely continuous vector fields to vector fields with \(A\)-proper mappings in Banach spaces. As application the problem \[ x^{(k+1)}(t)=f(t,x(t),x'(t),\dots, x^{(k)}(t)), \qquad b(x)=0 \] in the space \(C^ k\) on the whole axis \(R\) is considered. Reviewer: P.Zabreiko (Minsk) MSC: 47H10 Fixed-point theorems Keywords:continuation method; completely continuous vector fields; vector fields with \(A\)-proper mappings in Banach spaces PDFBibTeX XMLCite \textit{W. Kryszewski}, Zesz. Nauk. Wydz. Mat. Fiz. Chem., Mat., Gdańsk 6, 43--53 (1987; Zbl 0776.47030)