An \(m\)-point boundary value problem of Neumann type for a \(p\)-Laplacian like operator. (Q1428430)

The authors study a nonlinear second-order ordinary differential equation \(L(x)=f\) in \([0,1]\) subject to a multipoint boundary condition of the form \(x'(0)=0\) and \(\theta(x'(1)) = \sum_{i=1}^{m-2}a_i \theta(x'(\xi_i))\), where \(\theta\) is a given function and \(a_i \in \mathbb{R}\), \(\xi_i \in (0,1)\) are given constants. Using degree theory, they prove existence theorems under suitable assumptions which are too complicated to be stated here. One problem that has to be overcome comes from the fact that all constants are solutions for the corresponding problem \(L(x)=0\).