On the existence of weak solutions of semilinear elliptic equations and systems with Hardy potentials

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F19%3A00109357" target="_blank" >RIV/00216224:14310/19:00109357 - isvavai.cz</a>
Result on the web
<a href="https://www.sciencedirect.com/science/article/pii/S0022039618304248?via%3Dihub" target="_blank" >https://www.sciencedirect.com/science/article/pii/S0022039618304248?via%3Dihub</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jde.2018.07.060" target="_blank" >10.1016/j.jde.2018.07.060</a>

Result language
angličtina
Original language name
On the existence of weak solutions of semilinear elliptic equations and systems with Hardy potentials
Original language description
Let Omega subset of R-N (N >= 3) be a bounded C-2 domain and delta(x) = dist (x, partial derivative Omega). Put L-mu = Delta + mu/delta(2) with mu > 0. In this paper, we provide various necessary and sufficient conditions for the existence of weak solutions to -L(mu)u = u(p) + tau in Omega, u = nu on partial derivative Omega, where mu > 0, p > 0, tau and nu are measures on Omega and partial derivative Omega respectively. We then establish existence results for the system {-L(mu)u = is an element of v(p) + tau in Omega, -L(mu)v = is an element of u (p) over tilde + tau in Omega, u = nu, v = (nu) over tilde on partial derivative Omega, where is an element of = +/- 1, p > 0, (p) over tilde > 0, tau and (tau) over tilde are measures on Omega, nu and (nu) over tilde are measures on partial derivative Omega. We also deal with elliptic systems where the nonlinearities are more general.
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
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OECD FORD branch
10101 - Pure mathematics

Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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