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

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

Let Omega subset of R-N (N &gt;= 3) be a bounded C-2 domain and delta(x) = dist (x, partial derivative Omega). Put L-mu = Delta + mu/delta(2) with mu &gt; 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 &gt; 0, p &gt; 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 &gt; 0, (p) over tilde &gt; 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.

Název v anglickém jazyce

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

Popis výsledku anglicky

Let Omega subset of R-N (N &gt;= 3) be a bounded C-2 domain and delta(x) = dist (x, partial derivative Omega). Put L-mu = Delta + mu/delta(2) with mu &gt; 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 &gt; 0, p &gt; 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 &gt; 0, (p) over tilde &gt; 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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2019

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

JOURNAL OF DIFFERENTIAL EQUATIONS

ISSN

0022-0396

e-ISSN

1090-2732

Svazek periodika

266

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

43

Strana od-do

833-875

Kód UT WoS článku

000449108500025

EID výsledku v databázi Scopus

2-s2.0-85050670528