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


Topological transversality; essential mappings; topological degree; fixed point theory; continuation theorems

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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


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Nonlinear Analysis: Theory, Methods & Applications

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MR: 94a:58028.

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[6] MAWmN J., Points fixes, points critiques et probl~mes aux limites, Les Presses de l’Universit6 de Montr6al (1985).
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[10] PRECUP R., Measure of noncompactness and second order differential equations with deviating argument, Studia Univ. Babes-Bolyai 34(2), 25-35 (1989).


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