Abstract

We consider the problem Deltau + 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 we fix p > N/(N - 2) and then let q approach (N + 2)/(N - 2), If we fix q and then let p be close enough to NI(N - 2) then no solutions exist. (C) 2000 Editions scientifiques et medicales Elsevier SAS.