Acta mathematica scientia,Series A ›› 2009, Vol. 29 ›› Issue (2): 406-415.

• Articles • Previous Articles     Next Articles

Application of the Diagonalization Method in the Robin Boundary Value Problem for the Vector Nonlinear Integro-differential Equations

  

  1. (Department of Computer, Fujian Broadcasting TV University, Fuzhou 350003)
  • Received:2007-12-13 Revised:2008-12-10 Online:2009-04-25 Published:2009-04-25

Abstract:

The singularly perturbed boundary value problem of scalar integro-differential equations was studied extensively by the differential inequality method. However, it is impossible to carry this method over to a corresponding
nonlinear vector integro-differential equation. Therefore, for n-dimensional vector integro-differential equations the problem has  not be solved fully. Here, the author studys this nonlinear vector problem by diagonalization method. Under appropriate conditions the existence of solution is proved and the asymptotic estimate is given as well.

Key words: Integro-differential equation, Singular perturbation,  Robin boundary value problem, Diagonalization method

CLC Number: 

  • 45J
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