Project Details
Abstract
In this project, we will use the Palais-Smale theory to prove the multiplicity of positive solutions of the quasilinear elliptic systems
I:(subcritical case) ∈++=Δ−++=Δ−−−−−)(,)()()()(12222NNqppNqppRHvuRinvvuzfvvzhvRinvuuzfuuzguβαβαβαβλεβααλε
where N ≥ 3 and λ>0, 2≤p<N, α>1, β>1, 1<q<p< βα+< p*=pN/(N-p).
II:(critical case) Ω∂==Ω++=Δ−Ω++=Δ−−−−−onvuinvvuzfvvzhvinvuuzfuuzguqpqp0)()()()(2222βαβαβαβλβααλ
where Ω is a bounded domain in NR, N 2p≥ and λ>0, α>1, β>1, 1<q<p< βα+=p*=pN/(N-p).
Recently, many authors studied the elliptic systems with subcritical or critical exponents, and they proved the existence of least energy positive solution or the existence of at least two positive solutions for these problems. In this project, we want to construct the k compact Palais-Smale sequences which are suitably localized in correspondence of k maximum points of f.
Project IDs
Project ID:PA10107-0257
External Project ID:NSC101-2115-M182-001
External Project ID:NSC101-2115-M182-001
Status | Finished |
---|---|
Effective start/end date | 01/08/12 → 31/07/13 |
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