A nonlinear dirichlet problem with nonhomogeneous boundary data

Abstract

Estimates on the number of solutions to a certain class of nonlinear elliptic boundary value problems are obtained as a function of boundary data. Of particular interest is that solutions normally expected for these kinds of problems when the derivative of the nonlinearity has large limits at + ∞ and the nonhomogeneous term has a large projection onto the principle eigenspace of the Laplacian, will disappear as positive boundary data is increased sufficiently