Positive solutions of superlinear semipositone nonlinear boundary value problems

In this paper, by topological methods, we investigate the global structures of positive solution set of the following semipositone 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. We also obtain the existence of multiple positive solutions of the above problem. The nonlinear term f(x,u)f(x,u) may be nonsingular and singular at x=0x=0 or x=1x=1, also may be negative for some values xx and uu, and λλ is a parameter.