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

✍ Scribed by C. Tarsi

• Publisher: Elsevier Science
• Year: 2007
• Tongue: English
• Weight: 171 KB
• Volume: 66
• Category: Article
• ISSN: 0362-546X
• DOI: 10.1016/j.na.2006.03.035

✦ Synopsis

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 u 2 * -1 and Ω is a bounded, strictly star-shaped domain in R N , 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.