Asymptotically Stable Solutions for a Nonlinear Functional Integral Equation

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• 作者：L. T. P. Ngoc ; N. T. Long
• 关键词：Fixed point theorem of Krasnosel’skii type ; Contraction mapping ; Completely continuous ; Asymptotically stable solution ; 47H10 ; 45G10 ; 47N20 ; 65J15
• 刊名：Acta Mathematica Vietnamica
• 出版年：2016
• 出版时间：March 2016
• 年：2016
• 卷：41
• 期：1
• 页码：1-24
• 全文大小：407 KB
• 参考文献：1.Avramescu, C.: Some remarks on a fixed point theorem of Krasnosel’skii. Electron. J. Qual. Theory Differ. Equ. 5, 1–15 (2003)
  2.Avramescu, C., Vladimirescu, C.: An existence result of asymptotically stable solutions for an integral equation of mixed type. Electron. J. Qual. Theory Differ. Equ. 25, 1–6 (2005)CrossRef MathSciNet
  3.Corduneanu, C.: Integral equations and applications. Cambridge University Press, New York (1991)CrossRef MATH
  4.Deimling, K.: Nonlinear functional analysis. Springer, NewYork (1985)CrossRef MATH
  5.Dhage, B.C., Ntouyas, S.K.: Existence results for nonlinear functional integral equations via a fixed point theorem of Krasnoselskii-Schaefer type. Nonlinear Studies 9, 307–317 (2002)MathSciNet MATH
  6.Lang, S.: Analysis, vol. II. Addison - Wesley, Reading, Mass., California London (1969)MATH
  7.Liu, Z., Kang, S.M., Ume, J.S.: Solvability and asymptotic stability of a nonlinear functional-integral equation. Appl. Math. Lett. 24(6), 911–917 (2011)CrossRef MathSciNet MATH
  8.Ngoc, L.T.P., Long, N.T.: On a fixed point theorem of Krasnosel’skii type and application to integral equations. Fixed Point Theory Appl. 2006, Article ID 30847, 24 pages (2006)
  9.Ngoc, L.T.P., Long, N.T.: Existence of asymptotically stable solutions for a nonlinear functional integral equation with values in a general Banach space. Nonlinear Analysis, Theory, Methods & Applications. Series A: Theory and Methods 74(18), 7111–7125 (2011)MathSciNet MATH
  10.Ngoc, L.T.P., Long, N.T.: Solving a system of nonlinear integral equations and existence of asymptotically stable solutions. Differ. Equ. Appl. 4(2), 233–255 (2012)MathSciNet MATH
  11.Purnaras, I.K.: A note on the existence of solutions to some nonlinear functional integral equations. Electron. J. Qual. Theory Differ. Equ. 17, 1–24 (2006)CrossRef
  
• 作者单位：L. T. P. Ngoc (1)
  N. T. Long (2)
  
  1. Nha Trang Educational College, 01 Nguyen Chanh Street, Nha Trang, Vietnam
  2. Department of Mathematics and Computer Science, University of Natural Science, Vietnam National University Ho Chi Minh City, 227 Nguyen Van Cu Street, District 5, Ho Chi Minh, Vietnam
  
• 刊物主题：Mathematics, general;
• 出版者：Springer Singapore
• ISSN：2315-4144

文摘

In this paper, the solvability and the existence of asymptotically stable solutions for a nonlinear functional integral equation are studied. The main tools are a fixed point theorem of Krasnosel’skii type, the dominated convergence theorem, and other results from functional analysis. In order to illustrate the result obtained here, an example is given. Keywords Fixed point theorem of Krasnosel’skii type Contraction mapping Completely continuous Asymptotically stable solution