Existence of solutions for nonlinear random operator equations in Banach spaces (Q1826217)

Some new existence theorems for nonlinear random equations with operators of monotone type are proved. In Section 3 we treat random operator equations in which the classical coercivity hypothesis is not present. In Section 4 we consider random Hammerstein equations and we prove two results; one for general abstract Hammerstein equations and another for a concrete random integral equation of this type. Our results extend to the random case corresponding deterministic results proved by \textit{S. Itoh} [Math. Ann. 236, 133-146 (1978; Zbl 0369.60077)], \textit{A. Kartsatos} [J. Integral Equations 8, 175-184 (1985; Zbl 0584.47054)], \textit{H. Brezis} and \textit{F. E. Browder} [Bull. Amer. Math. Soc. 81, 82-88 (1975; Zbl 0298.47030)] and \textit{W. V. Petryshyn} and \textit{P. M. Fitzpatrick} [Trans. Amer. Math. Soc. 160, 39-63 (1971; Zbl 0236.47057)].