On a class of Hammerstein integral equations

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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 {Mathematical expression} 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.

Original languageEnglish (US)
Pages (from-to)49-84
Number of pages36
JournalManuscripta Mathematica
Volume29
Issue number1
DOIs
StatePublished - Mar 1 1979
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics(all)

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