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Abstrakty
Nonlinear vector integral equations are considered. Solution estimates and solvability conditions are derived. Applications to the periodic boundary value problem are also discussed. Under some restrictions our results improve the well-known ones. The main tool in the paper is the recent estimates for the resolvent of Hilbert-Schmidt operators.
Wydawca
Czasopismo
Rocznik
Tom
Strony
187--200
Opis fizyczny
Bibliogr. 15 poz.
Twórcy
autor
- Department of Mathematics Ben Gurion University of the Negev P.O Box 653, Beer-Sheva 84105 Israel, gilmi@cs.bgu.ac.il
Bibliografia
- [1] Akhmerov, R. R., Kamenskii, M. I., Potapov, S. A., Rodkina, A. E., Sadovskii, B. N., Measures of Noncompactness and Condensig Operators (in Russian), “Nauka” Sibirsk, Novosibirsk, 1986.
- [2] Argyros, I. Polynomial Operator Equations in Abstract Spaces and applications, CRC Press, Boca Raton, FL, 1998.
- [3] Dunford, N., Schwartz, J. T., Linear Operators. Part I. General Theory, Wiley- Interscience Publishers, Inc., New York, Interscience Publishers, Ltd., London, 1958.
- [4] Gatica, J. A., Fixed point theorems for к-set contractions and pseudo-contractive mappings, J. Math. Anal. Appl., 46(3) (1974), 555-564.
- [5] Gil’, M. I., Norm Estimations for Operator-Valued Functions and Applications, Marcel Dekker, Inc., New York, 1995.
- [6] Gil’, M. L, Invertibility conditions and bounds for spectra of matrix integral operators, Monatsh. Math. 129 (2000), 15-23.
- [7] Gil’, M. L, Invertibility and spectrum localization of non-selfadjoint operators, Adv. in Appl. Math., 28 (2002), 1-19.
- [8] Krasnosel’skii, A. M., Asymptotics of Nonlinearities and Operator Equations, Birkhauser Verlag, Basel, 1995.
- [9] Krasnosel’skii, M. A., Zabreiko, P. P., Geometrical Methods in Nonlinear Analysis, Springer-Verlag, Berlin, 1984.
- [10] Mawhin, J., Topological Degree Methods in Nonlinear Boundary Value Problems, Amer. Math. Soc., Providence, RI, 1979.
- [11] Meyer-Nienberg, P., Banach Lattices, Springer-Verlag, Berlin, 1991.
- [12] O’Regan, D., Precup, R., Theorems of Leray-Schauder Type and Applications, Series in Mathematical Analysis and Applications 3, Cordon and Breach Science Publishers, Amsterdam, 2001.
- [13] Schaefer, H. Neue Existenzsatze in der Theorie nichtlinearer Integralgleichungen (in German), Ber. Verh. Sachs. Acad. Wiss. Leipzig. Math.-Nat. Kl. 101(7), 1955.
- [14] Zabreiko, P. P., Koshelev, A. I., Krasnosel’skii, M. A., Mikhlin, S. G., Rakovshik, L. S., Stetzenko, B. Ya., Integral Equations, Noordhoff, Leiden, 1975.
- [15] Zeidler, E., Nonlinear Functional Analysis, and its Applications, Springer-Verlag, New York, 1986.
Typ dokumentu
Bibliografia
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bwmeta1.element.baztech-article-LOD6-0014-0027