Abstract:In this note we consider the boundary value problem $y''=f(x,y,y')$ $ (x\in [0,X];X>0)$, $y(0)=0$, $y(X)=a>0$; where $f$ is a real function which may be singular at $y=0$. We prove an existence theorem of positive solutions to the previous problem, under different hypotheses of Theorem 2 of L.E. Bobisud [J. Math. Anal. Appl. {173} (1993), 69--83], that extends and improves Theorem 3.2 of D. O'Regan [J. Differential Equations {84} (1990), 228--251].
Keywords: ordinary differential equations, singular boundary value problem, positive solutions
AMS Subject Classification: 34B15