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Języki publikacji
Abstrakty
In this paper we study the existence of continuous solutions of quadratic integral equations. The theory of quadratic integral equations has many useful applications in mathematical physics, economics, biology, as well as in describing real world problems. The main tool used in our investigations is a fixed point result for the multivalued solution's map with acyclic values.
Czasopismo
Rocznik
Tom
Strony
433--440
Opis fizyczny
Bibliogr. 19 poz.
Twórcy
autor
autor
- Università di Firenze, Facoltà di Ingegneria Via S. Marta 3, 50139 Italy, giuseppe.anichini@unifi.it
Bibliografia
- [1] G. Anichini, G. Conti, Boundary value problem for implicit ODE’s in a singular case, Differential Equations and Dynamical Systems 7 (1999) 4, 437-456.
- [2] G. Anichini, G. Conti, Some properties of the solution set for integral non compact equations, accepted by Far East Journal of Mathematical Sciences, 2006.
- [3] J. Appell, P.P. Zabrejko, Nonlinear Superposition Operators, Cambridge Tracts in Mathematics, 95, Camb. Univ. Press, Cambridge, 1990.
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- [5] J. Banas, M. Lecko, W.G. El-Sayed, Existence theorems for some quadratic integral equations, J. Math. Anal. Appl. 222 (1998), 276–285.
- [6] Banas, J., Rocha Martin, J., Sadarangani, K. On solutions of a quadratic integral equation of Hammerstein type. Math. Comput. Modelling 43 (2006) 1–2, 97–104.
- [7] L.W. Busbridge, The Mathematics of Radiative Transfer, Cambridge Univ. Press, Cambridge, England, 1960.
- [8] J. Caballero, B. López, K. Sadarangani, Existence of nondecreasing and continuous solutions of an integral equation with linear modification of the argument, Acta Math. Sin. (Engl. Ser.) 23 (2007) 9, 1719–1728.
- [9] S. Chandrasekhar, Radiative transfer, Dover Publications, Inc., New York 1960.
- [10] M. Crum, On an integral equation of Chandrasekhar, Quart. J. Math. Oxford Ser. 2. 18 (1947), 244–252.
- [11] K. Czarnowski, T. Pruszko, On the structure of fixed point sets of compact maps in B0 spaces with applications to integral and differential equations in unbounded domain, J. Math. Anal. Appl. 154 (1991) 1, 151–163.
- [12] K. Deimling, Nonlinear Functional Analysis, Springer, Berlin, 1985.
- [13] A. Dold, Lectures on Algebraic Topology, Springer Verlag, Berlin, 1972.
- [14] P. Edström, A fast and stable solution method for the radiative transfer problem, SIAM Rev. 47 (2005) 3, 447–468.
- [15] L. Górniewicz, A. Granas, Fixed point theorems for multi-valued mappings of the absolute neighbourhood retracts, J. Math. Pures Appl. (9), 49 (1970), 381–395.
- [16] S. Hu, M. Khavanin, W. Zhuang, Integral equations arising in the kinetic theory of gases, Appl. Anal. 34 (1989), 281–286.
- [17] J. Lasry, R. Robert, Analyse nonlineaire multivoque, UER Math de la Decision no. 249, Paris Dauphine, 1979.
- [18] L.K. Nowosad, B.R. Saltzberg, On the solution of a quadratic integral equation arising in signal design, Journal of the Franklin Institute 281 (1966) 6, 437–454.
- [19] C.A. Stuart, Existence theorems for a class of nonlinear integral equations, Math. Z. 137 (1974), 49–66.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-AGH9-0005-0007