ON NONHOMOGENEOUS ELLIPTIC-EQUATIONS INVOLVING CRITICAL SOBOLEV EXPONENT

Let p = 2N/N-2, N greater-than-or-equal-to 3 be the limiting Sobolev exponent and OMEGA subset-of R(N) open bounded set. We show that for f is-an-element-of H-1 satisfying a suitable condition and f not-equal 0, the Dirichlet problem: [GRAPHICS] admits two solutions u0 and u1 in H-0(1)(OMEGA). Also u0 greater-than-or-equal-to 0 and u1 greater-than-or-equal-to 0 for f greater-than-or-equal-to 0. Notice that, in general, this is not the case if f = 0 (see [P]).