Bounds and decay results for some second-order semilinear elliptic problems
Lawrence Edward Payne, Philip W. Schaefer, J. C. Song · Mathematical Methods in the Applied Sciences · 1998
The asymptotic behaviour of solutions of certain semilinear elliptic Dirichlet boundary value problems defined on a semi-infinite cylinder is investigated by means of energy arguments and maximum principles. Various hypotheses are made on the form of the semilinear term, and in some cases it is found that the rate of decay of solutions is faster than the optimal decay rate for harmonic functions. © 1998 B. G. Teubner Stuttgart—John Wiley & Sons, Ltd.