Steady states of radially symmetric diffusion processes (Q1969068)

In the paper, the following class of degenerate and singular second-order differential equations is considered: \[ -(p(t,x)\varphi (x'))'=f(t,x,x'), \quad x(0)=x(1)=0, \] where the continuous functions \(p(t,x)\) and \(\varphi(t)\) possess some degeneracy and the function \(f\) possesses a singularity at \(x=0\). Applying Schauder`s fixed point theorem and a comparison principle to a suitable \(\varepsilon \) problem, the existence and uniqueness of a nonnegative (probably strong) solution to (1) is given. Some related results are cited, as for instance: \textit{D. O'Regan} [SIAM J. Math. Anal. 24, No.~8, 648-668 (1993; Zbl 0778.34013)], and \textit{J. A. Gatica, V. Oliker} and \textit{P. Waltman} [J. Differ. Equations 79, No.~1, 62-78 (1989; Zbl 0685.34017)].