The nonexistence of positive solutions is discussed for -△pu = a(x)uq-1 in Ω, u|∂Ωn = 0, for the case where a(x) is a bounded positive function and Ω is a strip-like domain such as Ω = Ωd x ℝN-d with Ωd bounded in ℝd. The existence of nontrivial solution of (E) is proved by Schindler for q ∈ (p,p*) where p* is Sobolev's critical exponent. Our method of proofs for nonexistence rely on the "Pohozaev-type inequality" (for q ≥ p*); and on a new argument concerning the simplicity of the first eigenvalue for (generalized) eigenvalue problems combined with translation invariance of the domain (for q ≤ p).
|Number of pages||14|
|Journal||Discrete and Continuous Dynamical Systems|
|Publication status||Published - 1997|
ASJC Scopus subject areas
- Applied Mathematics
- Discrete Mathematics and Combinatorics