Eigenvalues and the One-Dimensional p-Laplacian1

We consider the boundary value problem ϕp u + λF t u = 0, with p > 1, t ∈ 0 1 , u 0 = u 1 = 0, and with λ > 0. The value of λ is chosen so that the boundary value problem has a positive solution. In addition, we derive an explicit interval for λ such that, for any λ in this interval, the existence of a positive solution to the boundary value problem is guaranteed. In addition, the existence of two positive solutions for λ in an appropriate interval is also discussed