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@article{1698837,
author = {Bhakta, Mousomi and Nguyen, Phuoc Tai},
article_location = {Berlin},
article_number = {1},
doi = {http://dx.doi.org/10.1515/anona-2020-0060},
keywords = {nonlocal; system; existence; multiplicity; linking theorem; measure data; source terms; positive solution},
language = {eng},
issn = {2191-9496},
journal = {Advances in Nonlinear Analysis},
title = {On the existence and multiplicity of solutions to fractional Lane-Emden elliptic systems involving measures},
url = {https://doi.org/10.1515/anona-2020-0060},
volume = {9},
year = {2020}
}
TY - JOUR
ID - 1698837
AU - Bhakta, Mousomi - Nguyen, Phuoc Tai
PY - 2020
TI - On the existence and multiplicity of solutions to fractional Lane-Emden elliptic systems involving measures
JF - Advances in Nonlinear Analysis
VL - 9
IS - 1
SP - 1480-1503
EP - 1480-1503
PB - Walter de Gruyter GmbH
SN - 21919496
KW - nonlocal
KW - system
KW - existence
KW - multiplicity
KW - linking theorem
KW - measure data
KW - source terms
KW - positive solution
UR - https://doi.org/10.1515/anona-2020-0060
L2 - https://doi.org/10.1515/anona-2020-0060
N2 - We study positive solutions to the fractional Lane-Emden system {(-Delta)(s)u = v(p) + mu in Omega (-Delta)(s)v = u(q) + v in Omega (S) u = v = 0 in Omega(c) = R-N\Omega, where Omega is a C-2 bounded domains in R-N, s is an element of(0, 1), N > 2s, p > 0, q > 0 and mu, nu are positive measures in Omega. We prove the existence of the minimal positive solution of (S) under a smallness condition on the total mass of mu and nu. Furthermore, if p, q is an element of (1, N+s/N-s), 0 <= mu, nu is an element of L-r (Omega) for some r > N/2s, we show the existence of at least two positive solutions of (S). The novelty lies at the construction of the second solution, which is based on a highly nontrivial adaptation of Linking theorem. We also discuss the regularity of the solutions.
ER -
BHAKTA, Mousomi a Phuoc Tai NGUYEN. On the existence and multiplicity of solutions to fractional Lane-Emden elliptic systems involving measures. \textit{Advances in Nonlinear Analysis}. Berlin: Walter de Gruyter GmbH, 2020, roč.~9, č.~1, s.~1480-1503. ISSN~2191-9496. Dostupné z: https://dx.doi.org/10.1515/anona-2020-0060.
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