On the topological transversality principle

We propose a generalization of the topological transversality theorem of Granas [1] (see also [2]). We show the implication of this theorem in the axiomatic theory of the topological degree due to Amann and Weiss [3] (see also [4]) and its connection with the fixed point theory. Finally, as an application, we prove a continuation theorem for equations of the form

\(L(x) = N(x)\)

where \(L\) is a linear Fredholm mapping of index zero and \(N\) is a nonlinear mapping satisfying a compactness-like condition of Monch type. This theorem extends some continuation results due to Mawhin [5] (see also [6]) and Volkmann [7] and in a particular case reduces to a fixed point theorem of Monch [8].

Radu Precup
Babeş-Bolyai University, Department of Mathematics, Cluj-Napoca, Romania

R. Precup, On the topological transversality principle, Nonlinear Anal.: Theory, Meth. Appl., 20 (1993), 1-9. https://doi.org/10.1016/0362-546X(93)90181-Q

https://ictp.acad.ro/wp-content/uploads/2022/08/1993b-Precup-On-the-topological-transversality-principle.pdf

https://doi.org/10.1016/0362-546X(93)90181-Q

MR: 94a:58028.

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