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Inclusion of Regular and Singular Solutions of Certain Types of Integral Equations

  • Lothar Collatz
Part of the International Series of Numerical Mathematics book series (ISNM, volume 73)

Abstract

In the functional equation u=Tu for a function u (x) = u (x1, … , xn let the completely continuous linear or nonlinear operator T be “monotonically decomposible” in the sense of J. Schroder. We suppose, one has calculated, for instance with an iteration procedure an interval J = [v1,w1]which contains under certain conditions at least one solution u Schauders fixed point theorem. This is in many cases the only easily calculable possibility of an inclusion for u. This method is also applicable for calculation of solutions with certain types of singularities. Recently three-dimensional singuities in the three-dimensional space.

This method is also applicable for calculation of solutions with certain types of singularities. Recently three-dimensional singularities became more important. Numerical examples are given, also for distributed singularities in the three-dimensional space.

Keywords

Singular Solution Iteration Procedure Nonlinear Integral Equation Classical Fixed Point Nonlinear Vibra 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 1985

Authors and Affiliations

  • Lothar Collatz
    • 1
  1. 1.Institut für Angewandte Mathematik der Universität HamburgHamburg 13Germany

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