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We prove an existence theorems for the nonlinear integral equation... [formuła matematyczna]... where f, g, x are functions with values in Banach spaces. Our fundamental tools are: measures of noncompactness and properties of the Henstock-Kurzweil integral.
Wydawca
Rocznik
Tom
Strony
227--238
Opis fizyczny
bibliogr. 27 poz.
Twórcy
autor
- Faculty of Mathematics and Computer Science Adam Mickiewicz University Umultowska 87, 61-614 Poznań, Poland, anetas@amu.edu.pl
Bibliografia
- [1] R. P. Agarwal, M. Meehan and D. O'Regan, Positive solutions of singular integral equations - a survey, Dynam. Systems Appl. 14 (2005), no. 1, 1-37.
- [2] R.P. Agarwal, M. Meehan and D. O'Regan, Nonlinear Integral Equations and Inclusions, Nova Science Publishers, 2001.
- [3] R.P. Agarwal and D. O'Regan, Existence results for singular integral equations of Fredholm type, Appl. Math. Lett. 13 (2000), no 2, 27 - 34.
- [4] A. Alexiewicz, Functional Analysis, PWN, Warszawa 1969, in Polish.
- [5] A. Ambrosetti, Un teorema di esistenza per le equazioni differenziali negli spazi di Banach, Rend. Sem. Univ. Padova 39 (1967), 349-360.
- [6] J. Bana´s and K. Goebel, Measures of Noncompactness in Banach Spaces, Lecture Notes in Pure and Appl. Math. 60, Dekker , New York and Basel, 1980.
- [7] S.S. Cao, The Henstock integral for Banach valued functions, SEA Bull. Math. 16 (1992),36-40.
- [8] T.S. Chew, On Kurzweil generalized ordinary differential equations, J. Differential Equations 76 (1988), 286-293.
- [9] T.S. Chew and F. Flordeliza, On x0 = f(t, x) and Henstock-Kurzweil integrals, Differential and Integral Equations 4 (1991), 861-868.
- [10] R.A. Gordon, The Integrals of Lebesgue, Denjoy, Perron and Henstock, Amer. Math. Soc., Providence, R I 1994.
- [11] R.A. Gordon, Riemann integration in Banach spaces, Rocky Mountain J. 21 (1991), 923-949.
- [12] R. Henstock, The General Theory of Integration, Math. Monographs, Clarendon Press, Oxford, 1991.
- [13] G.L. Karakostas and P.h. Tsamatos, Multiple positive solutions of some integral equations arisen from nonlocal boundary - valued problems, Electron. J. Differential Equations 30 (2002), 1-17.
- [14] A. Karoui, Existence and approximate solutions of nonlinear equations, J. Inequal. Appl. 5 (2005), 569 - 581.
- [15] I. Kubiaczyk and A. Sikorska, Differential equations in Banach spaces and Henstock - Kurzweil integrals, Discuss. Math. Differ. Incl. 19 (1999), 35-43.
- [16] K. Kuratowski, Topologie, PWN, Polish Sci. Publ., Warszawa, 1958.
- [17] J. Kurzweil, Generalized ordinary differential equations and continuous dependence on a parameter, Czech. Math. J. 7 (1957), 642-659.
- [18] P.Y. Lee, Lanzhou Lectures on Henstock Integration, Ser. Real Anal. 2 World Sci., Singapore, 1989.
- [19] R.H. Martin, Nonlinear Operators and Differential Equations in Banach Spaces, Robert E.Krieger, Melbourne, FL, 1987.
- [20] M. Meehan and D. O'Regan, Positive solutions of singular and nonsingular Fredholm integral equations, J. Math. Anal. Appl. 240 (1999), no 2, 416 - 432.
- [21] R.K. Miller, J. A. Nohel and J.S. Wong, A stability theorem for nonlinear mixed integral equations, J. Math. Anal. Appl. 25 (1969), no. 2, 446 - 449.
- [22] H. M¨onch, Boundary value problems for nonlinear ordinary differential equations of second order in Banach spaces, Nonlinear. Anal. 4 (1980), 985 - 999.
- [23] D. O'Regan, Existence results for nonlinear integral equations, J. Math. Anal. Appl. 192 (1995), no. 3, 705 - 726.
- [24] D. O'Regan and M. Meehan, Existence Theory for Integral and Integrodifferential Equations, Mathematics and its Applications, 445, Kluwer Academic, Dordrecht, 1998.
- [25] A. Sikorska-Nowak, Retarded functional differential equations in Banach spaces and Henstock-Kurzweil integrals, Demonstratio Math. 35 (2002), 49-60.
- [26] A.P. Solodov, On conditions of differentiability almost everywhere for absolutely continuous Banach-valued function, Moscow Univ. Math. Bull. 54 (1999), 29-32.
- [27] G. Ye, P.Y. Lee and C. Wu, Convergence theorems of the Denjoy-Bochner, Denjoy-Pettis and Denjoy-Dunford integrals, SEA Bull. Math. 23 (1999), 135-140.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BUS5-0019-0014