In the recent past maily results have been established on non-negative solu tions to boundry value problems of the form u(0) = 0= u(1) where λ > 0, f(0) > 0 (positone problem). In this paper we consider the imp...In the recent past maily results have been established on non-negative solu tions to boundry value problems of the form u(0) = 0= u(1) where λ > 0, f(0) > 0 (positone problem). In this paper we consider the impact on the non-negative solutions when f(0) <0. We find that we need f(u) to be convex to guarantee uniquenness of positive solutions and f(u) to be appropriately concave for multiple positive solutions.展开更多
文摘In the recent past maily results have been established on non-negative solu tions to boundry value problems of the form u(0) = 0= u(1) where λ > 0, f(0) > 0 (positone problem). In this paper we consider the impact on the non-negative solutions when f(0) <0. We find that we need f(u) to be convex to guarantee uniquenness of positive solutions and f(u) to be appropriately concave for multiple positive solutions.