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, Volume 29, Issue 1, pp 49–84 | Cite as

On a class of Hammerstein integral equations

  • Horst R. Thieme
Article

Abstract

By a monotone representation of the nonlinearity we derive sufficient (and partly necessary) conditions for the unique existence of positive solutions of the Hammerstein integral equation
$$\begin{array}{*{20}c} {u(x) = \int\limits_D {f(y,u(y)) k(x,y) dy ,} } & {x \in D,} \\ \end{array} $$
and for the convergence of successive approximations towards the solution. Further we study the corresponding nonlinear eigenvalue problem. Essentially we assume that the integral kernel k satisfies appropriate positivity conditions and that, for the nonlinearity f and any y ∈ D, rf(y,r) strictly monotone increases and f(y,r)/r strictly monotone decreases as r>0 increases.

Keywords

Integral Equation Eigenvalue Problem Number Theory Algebraic Geometry Topological Group 
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 1979

Authors and Affiliations

  • Horst R. Thieme
    • 1
  1. 1.Mathematisches Institut der Westfälischen Wilhelms-UniversitätMünsterBundesrepublik Deutschland

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