On integrated Volterra integrodifferential equation of higher order

• Autorzy: Pachpatte B. G.
• Języki publikacji: EN

Abstrakty

EN

In this paper we study the existence and other properties of solutions of a certain iterated Volterra integrodifferential equation of higher order. The tools employed in the analysis are based on application of the Leray-Schauder alternative and a certain integral inequality which provides explicit bound on the unknown function.

Słowa kluczowe

EN

integrodifferential equation; higher order; Leray-Schauder alternative; integral inequality; initial-value problem; global existence; completely continuous operators; fixed point; r-derivatives

• Wydawca: Wydawnictwo Politechniki Poznańskiej
• Czasopismo: Fasciculi Mathematici
• Rocznik: 2008
• Tom: Nr 39
• Strony: 47--61
• Opis fizyczny: Bibliogr. 16 poz.

Twórcy

autor

Pachpatte B. G.

• 57 Shri Niketan Colony, Near Abhinay Talkies, Aurangabad 431 001 (Maharashtra), India,

Bibliografia

• [1]CONSTANTIN Α., Topological transversality: Application to an integrodifferential equation, J. Math. Anal. Appl., 197(1996), 855-863.
• [2]DUGUNDJI J., GRANAS A . , Fixed point theory, Gauthier-Villars, Warsaw 1982.
• [3]ESHMATOV KH., Averaging in some systems of integro-differential equations, DifferentsiaVnye Uravneniya (English translation), 10(6)(1974), 1124-1129.
• [4]HARDY G . H . , LITTLEWOOD J . E . , POLYA G . , Inequalities, Cambridge University Press, 1934.
• [5]LEE J. W., O'REGAN D . , Existence results for differential delay equations, I, J. Differential Equations, 102(1993), 342-359.
• [6]LOGINOV V.M., Averaging in integrodifferential equations of special type, DifferentsiaVnye Uravneniya (English translation), 14(10)(1978), 1875-1880.
• [7]MORCHALO J., Construction of upper and lower functions by approximate integration of an integrodifferential equation of higher order, Fasc. Math.,9(1975), 97-108.
• [8]NTOUYAS S.K., Initial and boundary value problems for functional differential equations via the topological transversality method: A survey, Bull. Greek.Math. Soc., 40(1998), 3-41.
• [9]PACHPATTE B . G . , On a nonlinear Volterra integrodifferential equation of higher order, Utilitas Mathematica, 27(1985), 97-109.
• [10]PACHPATTE B . G . , Applications of the Leray-Schauder alternative to some Volterra integral and integrodifferential equations, Indian J. Pure ApplMath.,26(12)(1995), 1161-1168.
• [11]PACHPATTE B . G . , Inequalities for Differential and Integral Equations, Mathematics in Science and Engineering series, Vol. 197, Academic Press, New York, 1998.
• [12]PACHPATTE B.G., Global existence and estimates for solutions of certain higher order differential equations, Studia Univ. Babes-Bolyai, Mathematica XLIV(3)(1999), 53-66.
• [13]PACHPATTE B.G., Mathematical Inequalities, North-Holland Mathematical Library, Vol. 67, Elsevier Science B.V., 2005.
• [14]PACHPATTE B . G . , Integral and Finite Difference Inequalities and Applications,North-Holland Mathematics Studies, Vol. 205, Elsevier Science B.V., 2006.
• [15]PACHPATTE B . G . , On higher order Volterra-Fredholm integrodifferential equation, Fasc. Math., 37(2007), 35-48.
• [16]WLNTNER A., The nonlocal existence problem for ordinary differential equations, Amer. J. Math., 67(1945), 277-284.