Articles

ON A NONLINEAR VOLTERRA-HAMMERSTEIN INTEGRAL EQUATION IN TWO VARIABLES

  • Le Thi Phuong Ngoc ,
  • Nguyen Thanh Long
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  • Nhatrang Educational College, 01 Nguyen Chanh Str., Nhatrang City, Vietnam; Department of Mathematics and Computer Science, University of Natural Science,Vietnam National;
    University Ho Chi Minh City, 227 Nguyen Van Cu Str., Dist. 5, Ho Chi Minh City, Vietnam

Received date: 2011-07-11

  Online published: 2013-03-20

Supported by

The authors are extremely grateful for the support given by Vietnam’s National Foundation for Science and Technology Development (NAFOSTED) under Project 101.01-2012.12.

Abstract

Using a fixed point theorem of Krasnosel’skii type, this article proves the exis-tence of asymptotically stable solutions for a Volterra-Hammerstein integral equation in two variables.

Cite this article

Le Thi Phuong Ngoc , Nguyen Thanh Long . ON A NONLINEAR VOLTERRA-HAMMERSTEIN INTEGRAL EQUATION IN TWO VARIABLES[J]. Acta mathematica scientia, Series B, 2013 , 33(2) : 484 -494 . DOI: 10.1016/S0252-9602(13)60013-2

References

[1] Avramescu C, Vladimirescu C. Asymptotic stability results for certain integral equations. Electronic J Diff Equat, 2005, 126: 1–10

[2] Avramescu C, Vladimirescu C. An existence result of asymptotically stable solutions for an integral equation of mixed type. Electronic J Qualitative Theory of Diff Equat, 2005, 25: 1–6

[3] Corduneanu C. Integral equations and applications. New York: Cambridge University Press, 1991

[4] Lang S. Analysis II. Addison-Wesley, Reading, Mass, California London, 1969

[5] Lungu N, Rus I A. On a functional Volterra-Fredholm integral equation via Picard operator. Journal of Mathematical Inequalities, 2009, 3(4): 519–527

[6] Ngoc L T P, Long N T. On a fixed point theorem of Krasnosel’skii type and application to integral equations. Fixed Point Theory and Applications, 2006, 2006: Article ID 30847, 24 pages

[7] Ngoc L T P, Long N T. Applying a fixed point theorem of Krasnosel’skii type to the existence of asymptot-ically stable solutions for a Volterra-Hammerstein integral equation. Nonlinear Analysis, Theory, Methods & Applications, Series A: Theory and Methods, 2011, 74(11): 3769–3774

[8] Pachpatte B G. On Fredholm type integral equation in two variables. Differential Equations & Applications, 2009, 1(1): 27–39

[9] Pachpatte B G. Volterra integral and integrodifferential equations in two variables. J Inequal Pure and Appl Math, 2009, 10(4): Art. 108, 10 pp

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