Positive solutions of sublinear Sturm–Liouville problems with changing sign nonlinearity

In this paper, the following nonlinear Sturm–Liouville problem {−(p(x)u′(x))′+q(x)u(x)=λf(x,u(x)),0≤x≤1,α0u(0)+β0u′(0)=0,α1u(1)+β1u′(1)=0 is discussed by topological methods. In the case that the nonlinear term is non-singular or singular, a global structure of the positive solution set of the above problem is obtained, and the existence of positive solutions is proved under the condition that the nonlinear term is allowed to change sign.