Eigenvalues for systems of fractional p-Laplacians
We study the eigenvalue problem for a system of fractional p-Laplacians, that is, (-Δp)ru=λαp|u|α-2u|v|β(-Δp)sv=λβp|u|α|v|β-2vu=v=0in Ω,in Ω,in Ωc=RNΩ. We show that there is a first (smallest) eigenvalue that is simple and has associated eigenpairs composed of positive and bounded functions. Moreove...
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| Lenguaje: | Inglés |
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Rocky Mountain Mathematics Consortium
2018
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| Acceso en línea: | Registro en Scopus DOI Handle Registro en la Biblioteca Digital |
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| LEADER | 07063caa a22006737a 4500 | ||
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| 001 | PAPER-25260 | ||
| 003 | AR-BaUEN | ||
| 005 | 20230518205717.0 | ||
| 008 | 190410s2018 xx ||||fo|||| 00| 0 eng|d | ||
| 024 | 7 | |2 scopus |a 2-s2.0-85054576252 | |
| 040 | |a Scopus |b spa |c AR-BaUEN |d AR-BaUEN | ||
| 100 | 1 | |a Del Pezzo, L.M. | |
| 245 | 1 | 0 | |a Eigenvalues for systems of fractional p-Laplacians |
| 260 | |b Rocky Mountain Mathematics Consortium |c 2018 | ||
| 506 | |2 openaire |e Política editorial | ||
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| 520 | 3 | |a We study the eigenvalue problem for a system of fractional p-Laplacians, that is, (-Δp)ru=λαp|u|α-2u|v|β(-Δp)sv=λβp|u|α|v|β-2vu=v=0in Ω,in Ω,in Ωc=RNΩ. We show that there is a first (smallest) eigenvalue that is simple and has associated eigenpairs composed of positive and bounded functions. Moreover, there is a sequence of eigenvalues λn such that λn→∞ as n→∞ . In addition, we study the limit as p→∞ of the first eigenvalue, λ1,p, and we obtain [λ1,p]1/p→Λ1,∞ as p→∞, where Λ1,∞=inf(u,v){max{[u]r,∞[v]s,∞}∥|u|Γ|v|1-Γ∥L∞(Ω)}=[1R(Ω)](1-Γ)s+Γr. Here, R(Ω):= maxx∈Ω dist(x,∂Ω) and [w]t,∞:=sup(x,y)∈Ω|w(y)-w(x)||x-y|t. Finally, we identify a PDE problem satisfied, in the viscosity sense, by any possible uniform limit along subsequences of the eigenpairs. Copyright © 2018 Rocky Mountain Mathematics Consortium. |l eng | |
| 593 | |a Departamento de Matematicas Y Estadistica, Av. Figueroa, Alcorta, 7350, Argentina | ||
| 593 | |a Conicet and Departamento de Matematica, Universidad de Buenos Aires, Pabellon I, Buenos Aires, Argentina | ||
| 690 | 1 | 0 | |a EIGENVALUE PROBLEMS |
| 690 | 1 | 0 | |a FRACTIONAL OPERATORS |
| 690 | 1 | 0 | |a P-LAPLACIAN |
| 700 | 1 | |a Rossi, J.D. | |
| 773 | 0 | |d Rocky Mountain Mathematics Consortium, 2018 |g v. 48 |h pp. 1077-1104 |k n. 4 |p Rocky Mt. J. Math. |x 00357596 |t Rocky Mountain Journal of Mathematics | |
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| 856 | 4 | 0 | |u https://hdl.handle.net/20.500.12110/paper_00357596_v48_n4_p1077_DelPezzo |y Handle |
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