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

In this paper we prove nonexistence results for some classes of nonlinear elliptic equations with critical growth of the form View the MathML source{−Δu=λg(x,u)+|u|2∗−2u,x∈Ωu>0x∈Ωu=0x∈∂Ω Turn MathJax on where 2∗=2N/(N−2)2∗=2N/(N−2), g(x,u)g(x,u) is a lower-order perturbation of u2∗−1u2∗−1 and ΩΩ is a bounded, strictly star-shaped domain in RNRN, N≥3N≥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=0λ=0, for N=3N=3 and N=4N=4.