Nonlinear random elliptic boundary value problem (Q1122225)

The author using his random fixed point theorem [Indian J. Pure Appl. Math. 11, 791-799 (1980; Zbl 0441.60067)] obtains an abstract result for a class of random operator equations of the type \(G(w;x(w),x(w))=z\) where G: \(\Omega\) \(\times Y\times X\to X^*\) is a random operator, \(\Omega\) a probability measure space, X, Y are Banach spaces and \(z\in X^*\) a given element. The result generalizes a theorem of \textit{F. E. Browder} [Trans. Am. Math. Soc. 117, 530-550 (1965; Zbl 0127.319)], and is applied to discuss the solvability of a random elliptic boundary value problem for a system of the form \[ A(w)x=\sum_{| \alpha | \leq m}(-1)^{| \alpha |}D^{\alpha}A_{\alpha}(w,t,x,...,D^ mx). \]