Infinitely many solutions for a class of resonant problems

摘要

We consider radially symmetric solutions for a class of resonant problems on a unit ball B subset of R-n around the origin triangle u + lambda(1)u + g(u) = f (r) for x is an element of B, u = 0 on partial derivative B.Here the function g(u) is periodic of mean zero, x is an element of R-n, r = x, lambda(1) is the principal eigenvalue of triangle on B. The problem has either infinitely many or finitely many solutions depending on the space dimension n. The situation turns out to be different for each of the following cases: 1 = 7.