Some multiplicity results for a class of nonlinear boundary value problems (Q1344026)

The authors consider a two-point boundary value problem for the differential equation \[ -u''= f(x, u)= \alpha u^ -+ \beta u^ ++ \nu(x, u),\qquad 0< x< 1. \] The objective is to determine the precise number of solutions when the problem is forced on the boundary in a variety of ways. Results for the Neumann and Dirichlet problems are extended to more general boundary conditions via a homotopy between Dirichlet and Neumann data.