Purnaras, I. K. A note on the existence of solutions to some nonlinear functional integral equations. (English) Zbl 1119.45002 Electron. J. Qual. Theory Differ. Equ. 2006, Paper No. 17, 24 p. (2006). The paper deals with the existence result for the following nonlinear functional integral equation \[ x(t)= q(t)+ \int^{a(t)}_0 k(t, s)f(s, x(b(s)))\,ds+ \int^{m(t)}_0 v(t, s)g(s, x(n(s)))\,ds,\tag{1} \] where \(t\in J= [0,1]\) and \(q\), \(a\), \(b\), \(k\), \(v\), \(m\), \(n\), \(f\), \(g\) are assumed to be real functions satisfying some conditions expressed in terms of measurability, continuity and Carathéodory condition. Using the technique of maximal solutions the author obtains a result on the existence of solutions of (1). No examples are given. Reviewer: J. Banaś (Rzeszów) Cited in 8 Documents MSC: 45G10 Other nonlinear integral equations 47N20 Applications of operator theory to differential and integral equations Keywords:nonlinear functional integral equation; maximal solutions PDFBibTeX XMLCite \textit{I. K. Purnaras}, Electron. J. Qual. Theory Differ. Equ. 2006, Paper No. 17, 24 p. (2006; Zbl 1119.45002) Full Text: DOI EuDML