Eigenvalues and the One-Dimensional p-Laplacian

AbstractWe 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