Continuation principles for coincidences


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, Cluj-Napoca, Romania



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R. Precup, Continuation principles for conincidences, Mathematica (Cluj), 39(62) 1997 no. 1, 103-110.


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Academie Roumaine

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[1] A. Capietto, J. Mawhin, F. Zanolin, A continuation approach to superlinear periodic boundary value problems, J. Differential Equaitons, 88 (1990), 347-395.
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[3] R.E. Gaines, J. Mawhin, Coincidence Degree and Nonlinear Differential Equaitons. Lecture Notes in Math. 568, Springer, Berlin, 1977.
[4] A. Granas, R.B. Guenther, J.W. Lee, Some general existence principles in the Caracterodory theory of nonlinear differential systems, J. Math. Pures Appl. 70 (1991), 153-196.
[5] W. Krawcewicz, Contribution a la theorie des equations non lineaires dans les espaces de Banach. Dissertationes Math. (Rozprawy Mat.) 263, 1988.
[6] J. Leray, I. Schauder, Topologie et equations fonctionnelles. Ann. Sci. Ecole Norm Sup. (3) 51 (1934), 45-78.
[7] R. Precup, A Granas type approach to some continuation theorems and periodic  boundary value problems with impulses. Topol. Methods Nonlinear Anal. 5 (1995), 385-396.
[8] R. Precup, Periodic solutions of superlinear singular ordinary differential equations. to appear.
[9] P. Volkann, Demonstration d’une theoreme de coincidence par la methode de Granas. Bull. Soc. Math. Belgique, Serie B, 36 (1984), 235-242.


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