Uniqueness and Generic Non-degeneracy on Strips
E.N. Dances · Advanced Nonlinear Studies · 2002
Abstract In this paper, we prove the uniqueness of the positive decaying solution of -Δu = u p - λu on S,u = 0 on ∂S where S is an infinite strip in R n and p > 1 but close to 1. We can use this and real analyticity to prove that for “most” p in (1, (n + 2)/(n - 2)) our problem has a nondegenerate positive decaying solution.