NODAL SOLUTIONS FOR LANE-EMDEN PROBLEMS IN ALMOST-ANNULAR DOMAINS

In this paper, we prove an existence result to the problem-Delta u = vertical bar u vertical bar(p-1)u in Omega,u = 0 on partial derivative Omega,where Omega is a bounded domain in R-N which is a perturbation of the annulus. Then there exists a sequence p(1) < p(2) < center dot center dot center dot with lim pk(k ->+infinity) = +infinity such that for any real number p > 1 and p not equal p(k) there exist at least one solution with m nodal zones. In doing so, we also investigate the radial nodal solution in an annulus: we provide an estimate of its Morse index and analyze the asymptotic behavior as p -> 1.