Positive solutions of superlinear semipositone nonlinear boundary value problems~☆

摘要

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, α_0u(0) + β_0u~'(0) = 0, α_1u(l) + β_1u~'(l) = 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 λ is a parameter.