On the existence and multiplicity of solutions to fractional Lane-Emden elliptic systems involving measures

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F20%3A00114502" target="_blank" >RIV/00216224:14310/20:00114502 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1515/anona-2020-0060" target="_blank" >https://doi.org/10.1515/anona-2020-0060</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1515/anona-2020-0060" target="_blank" >10.1515/anona-2020-0060</a>

Result language
angličtina
Original language name
On the existence and multiplicity of solutions to fractional Lane-Emden elliptic systems involving measures
Original language description
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-NOmega, 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.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GJ19-14413Y" target="_blank" >GJ19-14413Y: Linear and nonlinear elliptic equations with singular data and related problems</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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