Positive solutions for nonlinear singular boundary value problems on the half line

Abstract

We discuss the existence of positive solutions for singular second order boundary value problems x'' = ?f(t, x, x'), ax(0) ? bx'(0) = k ? 0, x'(?) = 0, where f may be singular at x = 0 and x' = 0 and can change sign. Via fixed point theory, we establish the existence of positive solutions under some conditions on f. Our results deal with the situation where the solutions approach the singularities of the equation.