Continuation theorems for maps of Caristi type


The paper is devoted to the solvability of semilinear operator equations in Banach spaces, via continuation methods. Instead of degree methods, the author makes use of the notion of essential map. A no-degree version of an important continuation principle due to A. Capietto, J. L. Mawhin and F. Zanolin [J. Differential Equations 88 (1990), no. 2, 347–395; MR1081252] is also given.


Radu Precup
Babes-Bolyai University


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Radu Precup, Continuation principles for coincidences, Mathematica (Cluj) 39 (62), no. 1 (1997), 103-110. MR: 99c:47103.Continuation principles for coincidences, Mathematica (Cluj) 39 (62), no. 1 (1997), 103-110. MR: 99c:47103.


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Universitatea ”Babeș-Bolyai” Cluj-Napoca


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[1] J. Caristi, Fixed point theorems for mappings satisfying inwardness condition, Trans. Amer. Math. Soc. 215 (1976), 241-251.
[2] M. Frigon, A. Granas, Resultats du type de leray-Schauder pour des contractions  multivoques, Topol. Methods Nonlinear Anal.4 (1994), 197-208.
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[4] J. Mawhin, M. Willem, Critical Point Theory and Hamiltonian Systems, Springer-Verlag, Berlin, 1989.
[5] R. Precup, On the continuation principle for nonexpansive maps, Studia Univ. Babes-Bolyai/Mathematica 41, no.3 (1996), in print.
[6] R. Precup, Existence theorems for nonlinear by continuationmethods, in Proceedings of the Second World Congress of Nonlinear Analysis, Athena, Grecee, July 10-17, 1996 (ed. V. Lakshmikantham), Elsevier Science, to apppear.
[7] I.A. Rus, Metrical Fixed Point Theorem, Univ. of Cluj, Cluj, 1979.

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