Eigenvalues and the one-dimensional p-Laplacian

We consider the boundary value problem (phi(p)(u)) + lambdaF(t, u) = 0, with p 1, t epsilon (0, 1), u(0) = u(1) = 0, and with lambda 0. The value of lambda is chosen so that the boundary value problem has a positive solution. In addition, we derive an explicit interval for lambda such that, for any lambda 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 lambda in an appropriate interval is also discussed. (C) 2002 Elsevier Science (USA).