Multiple critical points of perturbed symmetric strongly indefinite functionals

We prove that the elliptic system -Delta u = vertical bar v vertical bar(q-2)v+k(x), x is an element of Omega, -Delta v=vertical bar u vertical bar(p-2)u+h(x), x is an element of Omega, where Omega is a regular bounded domain of R-N, N >= 3 and h, k is an element of L-2(Omega), admits an unbounded sequence of solutions (u(k), v(k)) is an element of H-0(1)(Omega) x H-0(1)(Omega), provided 2 < p <= q and N/2 (1-1/p-1/q) < p- 1/p. We also prove a generic multiplicity result for exponents in the open region bounded by the lines p = 2, q = 2 and the critical hyperbola. (c) 2008 Elsevier Masson SAS. All rights reserved.