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

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

Let Omega be a C-2 bounded domain in R-N (N &gt;= 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 &lt; mu &lt; C-H (Q), rho is a positive parameter, nu is a positive Radon measure on partial derivative Omega with norm 1 and 1 &lt; p &lt; 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 &lt; rho &lt;= rho*, and no positive solution if rho &gt; 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 &lt; rho &lt; 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.

Název v anglickém jazyce

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

Popis výsledku anglicky

Let Omega be a C-2 bounded domain in R-N (N &gt;= 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 &lt; mu &lt; C-H (Q), rho is a positive parameter, nu is a positive Radon measure on partial derivative Omega with norm 1 and 1 &lt; p &lt; 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 &lt; rho &lt;= rho*, and no positive solution if rho &gt; 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 &lt; rho &lt; 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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GJ19-14413Y" target="_blank" >GJ19-14413Y: Lineární a nelineární eliptické rovnice se singulárními daty a související problémy</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2021

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

—

Svazek periodika

304

Číslo periodika v rámci svazku

December

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

44

Strana od-do

29-72

Kód UT WoS článku

000704512500002

EID výsledku v databázi Scopus

2-s2.0-85116397035