Multiplicity and uniqueness for Lane-Emden equations and systems with Hardy potential and measure data

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F21%3A00119309" target="_blank" >RIV/00216224:14310/21:00119309 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1016/j.jde.2021.09.037" target="_blank" >https://doi.org/10.1016/j.jde.2021.09.037</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jde.2021.09.037" target="_blank" >10.1016/j.jde.2021.09.037</a>

Result language
angličtina
Original language name
Multiplicity and uniqueness for Lane-Emden equations and systems with Hardy potential and measure data
Original language description
Let Omega be a C-2 bounded domain in R-N (N >= 3), delta(x) = dist(x, partial derivative Omega) and C-H(Omega) be the best constant in the Hardy inequality with respect to Q. We investigate positive solutions to a boundary value problem for Lane-Emden equations with Hardy potential of the form -Delta u - mu/delta(2) u = u(p) in Omega, u = rho nu on partial derivative Omega, (P-rho) where 0 < mu < C-H (Q), rho is a positive parameter, nu is a positive Radon measure on partial derivative Omega with norm 1 and 1 < p < N-mu, with N-mu being a critical exponent depending on N and mu. It is known from [22] that there exists a threshold value rho* such that problem (P-rho) admits a positive solution if 0 < rho <= rho*, and no positive solution if rho > rho*. In this paper, we go further in the study of the solution set of (P-rho). We show that the problem admits at least two positive solutions if 0 < rho < rho* and a unique positive solution if rho= rho*. We also prove the existence of at least two positive solutions for Lane-Emden systems {- Delta u - mu/delta(2) u = v(p) in Omega, - Delta v - mu/delta(2) v = u(q) in Omega, u = rho nu, v = sigma tau on Omega, under the smallness condition on the positive parameters rho and sigma.
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
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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