Initial value problems for second-order integro-differential equations on unbounded domains in Banach space

• Autorzy: Liu Y.
• Języki publikacji: EN

Abstrakty

EN

In this paper, the Monch fixed point theorem is used to investigate the existence of solutions of initial value problem (IVP, for short) for second order nonlinear integro-differential equations on infinite intervals in a Banach space. At the same time, the uniqueness of solution for IVP is obtained also.

Słowa kluczowe

EN

initial boundary value problems; integro-differential equation; fixed-point theorems; relatively compact

PL

zagadnienia brzegowe; równania różniczkowe; punkt stały; przestrzeń Banacha

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2005
• Tom: Vol. 38, nr 2
• Strony: 349--364
• Opis fizyczny: Bibliogr. 8 poz.

Twórcy

autor

Liu Y.

• Department of Mathematics, Shandong Normal University, Jinan, 250014, P.R. China

Bibliografia

• [1] V. Lakshmikantham, Some problems in integro-differential equations of Volterra type, J. Integral Equations, Suppl. 10 (1985), 137-146.
• [2] D. Guo, V. Lakshmikantham, X. Liu, Nonlinear Integral Equations in Abstract Spaces, Kluwer Academic Publishers, 1996.
• [3] D. Guo, Initial value problems for second-order integro-differential equations in Banach spaces, Nonlinear Anal. 37 (1999), 289-300.
• [4] D. Guo, Second-order integro-differential equations of Volterra type on unbounded domains in Banach spaces, Nonlinear Anal. 41 (2000), 465-476.
• [5] D. Guo, V. Lakshmikantham, Nonlinear Problems in Abstract Cones, Academic Press, Inc., New York, 1988
• [6] V. Lakshmikantham and S. Leela, Nonlinear Differential Equations in Abstrad Space, Pergamon Oxford 1981.
• [7] Y. Liu, Boundary value problems for second order differential equations on unbounded domains in a Banach space, Appl. Math. Comput. 135 (2003), 569-583.
• [8] L. Liu, Iterative method for solutions and coupled quasi-solutions of nonlinear Fredholm integral equations in ordered Banach spaces, Indian J. Pure Appl. Math., 27 (1996), 959-972.