×

Some remarks on the continuation method in the fixed point theory. (English) Zbl 0776.47030

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
PDFBibTeX XMLCite