One-Dimensional Nonlinear Laplacians under a 3-Point Boundary Condition

We consider a three-point boundary value problem for operators such as the one-dimensionalp-Laplacian, and show when they have solutions or not, and how many. The inverse operatorsare given by various formulas involving zeros of a real-valued function. They are shown to be orderpreserving,for some parameter values, and non-singleton valued for others. The operators are shownto be m-dissipative in the space of continuous functions.