Charles University in Prague, Faculty of Mathematics and Physics
Abstract
summary:In this note we consider the boundary value problem y′′=f(x,y,y′)(x∈[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]