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)=@lf(x,u(x)),0@?x@?1,@a"0u(0)+@b"0u^'(0)=0,@a"1u(1)+@b"1u^'(1)=0. We also obtain the existence of multiple positive solutions of the above problem. The nonlinear term f(x,u) may be nonsingular and singular at x=0 or x=1, also may be negative for some values x and u, and @l is a parameter.