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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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