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Tytuł artykułu

On Volterra-Fredholm integral equation in two variables

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The aim of this paper is to study thexistence, uniqueness and other properties of solution of a certain Volterra-Fredholm integral equation in two independent variables. The main tools employed in the analysis are based on the applications of the well known Banach fixed point theorem and the new integral inequality with explicit estimate.
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839--852
Opis fizyczny
Bibliogr. 20 poz.
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Bibliografia
  • [1] S. Aširov and Ja. D. Mamedov, Investigation of solutions of nonlinear Volterra-Fredholm operator equations, Dokl. Akad. Nauk. SSSR 229 (1976), 982-986.
  • [2] P. R. Beesack, Systems of multidimensionai Volterra integral equations and inequalities, Nonlinear Analysis TMA 9 (1985), 1451-1486.
  • [3] A. Bielecki, Un remarque sur l'application de la méthode de Banach-Cacciopoli-Tikhonov dans la theorie de l'equations = f (x,y,z,p,q), Bull. Acad. Poln. Sci. Math. Phys. Astr. 4 (1956), 265-268.
  • [4] T. A. Burton, Volterra Integral and Differential Eguations, Academic Press, New York, 1983.
  • [5] C. Corduneanu, Integral Equations and Applications, Cambridge University Press, 1991.
  • [6] Z. Kamont and M. Kwapisz, On nonlinear Volterra integral-functional equations in several variables, Ann. Polon. Math. 40 (1981), 1-29.
  • [7] M. Kwapisz, On the exstence and uniqueness of integrable solutions for integral equations in several variables, Libertas Math. 9 (1989), 37-40.
  • [8] M. Kwapisz, Weighted norms and existence and uniqueness of Lp solutions for integral equations in several variables, J. Differential Equations 97 (1992), 246-262.
  • [9] M. Kwapisz and J. Turo, Some integral-functional equations, Funkcial Ekvac. 18 (1975), 107-162.
  • [10] M. A. Krasnoselskii, Topological Methods in the Theory of Nonlinear Integral Equations, Pergamon Press, Oxford, 1964.
  • [11] R. K. Miller, Nonlinear Volterra Integral Equations, W.A. Benjamin, Menlo Park CA, 1971.
  • [12] R. K. Miller, J. A. Nohel and J. S. W. Wong, A stability theorem for nonlinear mixed integral equations, J. Math. Anal. Appl. 25 (1969), 446-449.
  • [13] J. A. Nohel, Asymptotic relationships between systems of Volterra equations, Ann. Mat. Pura Appl. XC (1971), 149-165.
  • [14] B. G. Pachpatte, On some applications of Ważewski method for raultiple Volterra integral equations, An. Sti. Univ. Al. I. Guza Iaşi 29 (1983), 75-83.
  • [15] B. G. Pachpatte, On a nonlinear functional integral equation in two independent variables, An. Sti. Univ. Al. I. Guza Iaşi 30 (1984), 31-38.
  • [16] B. G. Pachpatte, Inequalities for Differential and Integral Equations, Academic Press, New York, 1998.
  • [17] B. G. Pachpatte Integral and Finite Difference Inequalities and Applications, North-Holland Mathematics Studies Vol. 205, Elsevier Science, B.V. 2006.
  • [18] M. B. Suryanarayana, On multidimensional integral equations of Volterra type Pacific J.Math. 41 (1972), 809-828.
  • [19] W. Walter, On nonlinear Volterra integral equations in several variables J. Math. Mech. 16 (1967), 967-985.
  • [20] W. Walter, Differential and Integral Inequalities, Springer-Verlag, Berlin, New York 1970.
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Bibliografia
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bwmeta1.element.baztech-article-PWA5-0022-0010
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