In this paper, we establish a sufficient condition for the existence of positive solutions of problem where 0 <α, 0 < q, 0 < λ, 1 < p and , is a bounded domain with C1,γ boundary for some γ∈ (0, 1).
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.
