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A note on the existence of solutions to some nonlinear functional integral equations. (English) Zbl 1119.45002

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.

MSC:

45G10 Other nonlinear integral equations
47N20 Applications of operator theory to differential and integral equations
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