Multiple solutions of some semilinear elliptic equations in slender cylindrical domains (Q1205272)

The authors consider a semilinear elliptic boundary value problem on a cylindrical domain when the height \(L\) of the cylinder may go to infinity; they prove results about the convergence as \(L\to\infty\) of solutions of the given elliptic problem with Dirichlet boundary data to the solution of the same problem on the cross sectional domain of the cylinder. They give necessary and sufficient conditions such that this convergence is true on part of the cylinder. Also, they analyze associated bifurcation and stability problems. The main ingredients of the proofs of their results are the various maximum principles of elliptic theory, the method of sub- and super-solutions, and variational principles.