The Coefficient Functions Affect the Multiplicities of Positive Solutions for Quasilinear Elliptic Systems

Project: National Science and Technology CouncilNational Science and Technology Council Academic Grants

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
StatusFinished
Effective start/end date01/08/1231/07/13

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