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On higher order Volterra-Fredholm integrodifferential equation

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EN
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EN
In the present paper we study the existence, uniqueness and other properties of soltions of a certain higher order Volterra-Fredholm integrodifferential equation. The well known Banach fixed point theorem coupled with Bilecki type norm and the new integral inequality with explicit estimate are used to establish the results.
Rocznik
Tom
Strony
35--48
Opis fizyczny
Bibliogr. 15 poz.
Twórcy
Bibliografia
  • [1] BIELECKI A., Une remarque sur la method de Banach-Cacciopoli-Tikhonov dans la theorie das equations differentielles ordinaries. Bull. Acad. Polon. Sci. Ser. Sci. Math. Phys. Astr., 4(1956), 261-264.
  • [2] CORDUNEANU C.. Bielecki's method in the theory of integral equations, Ann. Univ. 'Mariae-Curie-Sklodowska', section A, 38(1984), 23-40.
  • [3] CORDUNEANU C., Integral Equations and Applications, Cambridge University Press, 1991.
  • [4] HALLAM T.G., Asymptotic behavior of the solutions of a nonhomogeneous singular equation, J. Differential Equations. 3(1967), 135-152.
  • [5] KIKODZE M.S., The problem of uniqueness of solutions of the Cauchy problem and convergence of successive approximations, Differentsial'nye Uravneniya (English translation), 2(1966), 804-807.
  • [6] KRASNOSELSKII M.A., Topological Methods in the Theory of Nonlinear Integral Equations, Pergaman Press, Oxford 1964.
  • [7] KUSANO T., TRENCH W.F., Existence of global solutions with precribed asymptotic behavior for nonlinear ordinary differential equations, Ann. di Mat. Pura Appl., CXLII(1985), 381-392.
  • [8] MORCHAŁO J., Construction of upper and lower functions by approximate integration of an integrodifferential equation of higher order, Fasciculi Math-ematici, 9(1975), 97-108.
  • [9] PACHPATTE B.C., On a nonlinear Volterra integrodifferential equation of higher order, Utilitas Mathematica, 27(1985), 97-109.
  • [10] PACHPATTE B.C., Inequalities for Differential and Integral Equations, Academic Press, New York 1998.
  • [11] PACHPATTE E.G., Integral and Finite Difference Inequalities and Applications, North-Holland Mathematics Studies, Vol. 205, Elsevier Sicne, BV. 2006.
  • [12] PACHPATTE D.B., PACHPATTE B.C., Existence of global solutions for some higher order differential and integrodifferential equations, Fasc. Math., 27(1997), 67-79.
  • [13] TRENCH W.F., Asymptotic behavior of solutions of Lu = g (t,u, ....u(n-1) J. Differential Equations, 11(1972), 38-48.
  • [14] WALTMAN P., On the asymptotic behavior of solutions of n-th order equation, Monatsh. Fur. Math., 69(1965), 427-430.
  • [15] WEND D.V.V., Uniqueness of solutions of ordinary differential equations, Amer.Math.Monthly, 74(1967), 948-950.
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Bibliografia
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bwmeta1.element.baztech-article-BPP1-0069-0080
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