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An existence theorem of positive solutions to a singular non- linear boundary value problem

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Gabriele Bonanno

An existence theorem of positive solutions to a singular non- linear boundary value problem

Comment.Math.Univ.Carolinae 36,4 (1995) 609-614.

Abstract: In this note we consider the boundary value problemy00 =f(x, y, y0) (x ∈ [0, X];X > 0), y(0) = 0, y(X) = a > 0; where f is a real function which may be singular aty = 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, pos- itive solutions

AMS Subject Classification: 34B15

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