The existence theorems of the random solutions for random Hammerstein type nonlinear integral equations
Under certain conditions, existence of a nonnegative, not identically vanishing, random continuous solution \(\varphi (\omega,x)\) is proved for the random nonlinear Hammerstein integral equation \[ \varphi= \int_G k(\omega,x, y)f(y,\varphi) dy \] where \(f(x,u)= \sum^n_{i=1} a_i(x) u^{a_i}\), \(a_i>0\), \(a_i(x)\geq 0\), and \(G\) is a bounded closed domain in \(R^N\).
random nonlinear Hammerstein integral equation
scientific article; zbMATH DE number 1531189