A comparison theorem for second order ODEs and applications to singular problems (Q1345304)

The author studies existence and uniqueness questions for the nonlinear boundary value problem \(x'' + f(t,x,x') = 0\), \(x'(0) = x(1) = 0\). The approach is based on a comparison result. In the ``regular'' case, he obtains a uniqueness result which improves results of \textit{A. Granas}, \textit{R. B. Guenther} and \textit{J. W. Lee} [Pac. J. Math. 2, 1-16 (1971)], \textit{W. V. Petryshyn} [Pac. J. Math. 122, 169-195 (1986; Zbl 0585.34020)], and the author [Commentat. Math. Univ. Carol. 29, 285-291 (1988; Zbl 0667.34026)]. In the singular case he improves some results of \textit{J. V. Baxley} [SIAM J. Math. Anal. 22, 463-479 (1990; Zbl 0719.34038)], \textit{A. M. Fink}, \textit{J. A. Gatica}, \textit{G. E. Hernandez} and \textit{P. Waltman} [SIAM J. Math. Anal. 22, 440-462 (1991; Zbl 0722.34015)] and \textit{D. O'Regan} [Nonlinear Anal., Theory Methods Appl. 15, 1097-1109 (1990; Zbl 0732.34021)].