Uniqueness of positive solutions for quasilinear boundary value problems (Q1352367)

Motivated by the study of radially symmetric solutions of nonlinear elliptic equations, which involve the \(p-\)Laplacian operator in annular domains, the authors give some sufficient conditions for the uniqueness of positive solutions of some quasilinear differential equations of the type \[ (|u'|^{m-2}u')' + f(t,u,u') = 0, \;t_{1} < t < t_{2}, \;m \geq 2, \] under one of the boundary conditions: \[ u(t_{1}) = \xi_{1} \geq 0, \;u'(t_{2}) = \xi_{2} \geq 0, \;u'(t_{1}) = \xi_{1} \leq 0, \] \[ \;u(t_{1}) = \xi_{1} \geq 0, \;u(t_{2}) = \xi_{2} \geq 0, \] \[ u(t_2) = \xi_2\geq 0. \] The question about the existence of such solutions is treated in some previous papers by \textit{H. G. Kaper, M. Knaap} and \textit{M. K. Kwong} [Differ. Integral Equations 4, No. 3, 543-554 (1991; Zbl 0732.34019)] and \textit{M. del Pino, M. Elgueta} and \textit{R. Manasevich} [J. Differ. Equations 80, No. 1, 1-13 (1989; Zbl 0708.34019)].