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Nondecreasing solutions of a quadratic integral equation of Urysohn type on unbounded interval. (English) Zbl 1216.47116

By using a fixed point theorem of Darbo type, the author proves the existence of nondecreasing solutions in the Fréchet space C( + ) for the nonlinear integral equation of Urysohn type

x(t)=g(t)+f(t,x(t)) 0 u(t,τ,x(τ))dτ,t + =[0,)·

MSC:
47N20Applications of operator theory to differential and integral equations
47H08Measures of noncompactness and condensing mappings, K-set contractions, etc.
47B38Operators on function spaces (general)
47H30Particular nonlinear operators