Positive solutions for a class of boundary value problems on infinite intervals
Results concerning the existence of nonnegative solutions of the boundary value problem \({1 \over p(t)} (p(t)y')' = q(t)f(t,y,p(t)y')\), \(0 < t < \infty\), \(\lim_{t \to 0+} p(t)y'(t) = 0\) on \[ -\alpha y(0) + \beta \lim_{t \to 0+} p(t)y'(t) = 0,\;\alpha > 0,\;\beta > 0,\;\lim_{t \to \infty} y(t) = 0, \] are established by employing usual techniques. Examples are given to illustrate the results. The motivation for the present work has come from the works of \textit{F. V. Atkinson} and \textit{L. A. Peletier} [Arch. Ration. Mech. Anal. 93, 103-127 (1986; Zbl 0606.35029)] and \textit{K. Mcleod} and \textit{J. Serrin} [Arch. Ration. Mech. Anal. 99, 115-145 (1987; Zbl 0667.35023)].
scientific article; zbMATH DE number 736836
scientific article