Nonexistence results for a class of nonlinear elliptic equations involving critical Sobolev exponents

In this paper we prove nonexistence results for some classes of nonlinear elliptic equations with critical growth of the form where 2*=2N/(N−2), g(x,u) is a lower-order perturbation of u2*−1 and Ω is a bounded, strictly star-shaped domain in , N≥3. Combining Pohozaev’s identity with classical and weak interpolation inequality, we are able to exhibit examples of nonlinear problems without any (nontrivial) solution bifurcating from infinity in λ=0, for N=3 and N=4.