Abstract

We consider the problem: {Delta u + u(p) + u(q) = 0 in R-N, {0 < u(x) --> 0 as -x- --> + infinity, where 1 < p < N+2/N-2 < q. We prove that if q is fixed and we let p approach N+2/N-2 from below, then this problem has a large number of radial solutions. A similar fact takes place if one fixes p > N/N-2 and then lets q approach N+2/N-2. If y is fixed and p gets close enough to N/N-2 then no solution exists. (C) 2000 Academie des sciences/Editions scientifiques et medicales Elsevier SAS.