Semilinear elliptic equations with Hardy potential and
subcritical source term

J 2017

Semilinear elliptic equations with Hardy potential and subcritical source term

NGUYEN, Phuoc-Tai

Základní údaje

Originální název

Semilinear elliptic equations with Hardy potential and subcritical source term

Autoři

NGUYEN, Phuoc-Tai

Vydání

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, Germany, Springer, 2017, 0944-2669

Další údaje

Jazyk

angličtina

Typ výsledku

Článek v odborném periodiku

Obor

10101 Pure mathematics

Stát vydavatele

Německo

Utajení

není předmětem státního či obchodního tajemství

Odkazy

URL

Impakt faktor

Impact factor: 1.741

Označené pro přenos do RIV

Organizační jednotka

Přírodovědecká fakulta

DOI

https://doi.org/10.1007/s00526-017-1144-6

UT WoS

000401451700013

Klíčová slova anglicky

Hardy potential;Martin kernel;normalized boundary trace;source terms

Štítky

RIV ne

Příznaky

Mezinárodní význam, Recenzováno

Změněno: 2. 5. 2019 15:56, Mgr. Tereza Miškechová

Anotace

V originále

Let Omega be a smooth bounded domain in R-N (N > 2) and delta(x) := dist (x, partial derivative Omega).Assume mu is an element of R+ nu is a nonnegative finite measure on partial derivative Omega and g is an element of C(Omega x R+). We study positive solutions of -Delta u - mu/delta(2) u = g(x, u) in Omega, tr* (u) = nu. (P) Here tr*(u) denotes the normalized boundary trace of u which was recently introduced by Marcus and Nguyen (Ann Inst H Poincare Anal Non Lineaire, 34, 69- 88, 2017). We focus on the case 0 < mu < C-H(Omega) (the Hardy constant for Omega) and provide qualitative properties of positive solutions of (P). When g(x, u) = u(q) with q > 0, we prove that there is a critical value q* (depending only on N, mu) for (P) in the sense that if q < q* then (P) possesses a solution under a smallness assumption on., but if q >= q* this problem admits no solution with isolated boundary singularity. Existence result is then extended to a more general setting where g is subcritical [see (1.28)]. We also investigate the case where g is linear or sublinear and give an existence result for (P).

Citovat

NGUYEN, Phuoc-Tai. Semilinear elliptic equations with Hardy potential and subcritical source term. CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS. Germany: Springer, 2017, roč. 56/2017, č. 2, s. 1-28. ISSN 0944-2669. Dostupné z: https://doi.org/10.1007/s00526-017-1144-6.

@article{1448816,
   author = {Nguyen, PhuocandTai},
   article_location = {Germany},
   article_number = {2},
   doi = {https://doi.org/10.1007/s00526-017-1144-6},
   keywords = {Hardy potential;Martin kernel;normalized boundary trace;source terms},
   language = {eng},
   issn = {0944-2669},
   journal = {CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS},
   title = {Semilinear elliptic equations with Hardy potential and subcritical source term},
   url = {https://link.springer.com/article/10.1007%2Fs00526-017-1144-6},
   volume = {56/2017},
   year = {2017}
}

TY  - JOUR
ID  - 1448816
AU  - Nguyen, Phuoc-Tai
PY  - 2017
TI  - Semilinear elliptic equations with Hardy potential and subcritical source term
JF  - CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS
VL  - 56/2017
IS  - 2
SP  - 1-28
EP  - 1-28
PB  - Springer
SN  - 09442669
KW  - Hardy potential;Martin kernel;normalized boundary trace;source terms
UR  - https://link.springer.com/article/10.1007%2Fs00526-017-1144-6
N2  - Let Omega be a smooth bounded domain in R-N (N > 2) and delta(x) := dist (x, partial derivative Omega).Assume mu is an element of R+ nu is a nonnegative finite measure on partial derivative Omega and g is an element of C(Omega x R+). We study positive solutions of -Delta u - mu/delta(2) u = g(x, u) in Omega, tr* (u) = nu. (P) Here tr*(u) denotes the normalized boundary trace of u which was recently introduced by Marcus and Nguyen (Ann Inst H Poincare Anal Non Lineaire, 34, 69- 88, 2017). We focus on the case 0 < mu < C-H(Omega) (the Hardy constant for Omega) and provide qualitative properties of positive solutions of (P). When g(x, u) = u(q) with q > 0, we prove that there is a critical value q* (depending only on N, mu) for (P) in the sense that if q < q* then (P) possesses a solution under a smallness assumption on., but if q >= q* this problem admits no solution with isolated boundary singularity. Existence result is then extended to a more general setting where g is subcritical [see (1.28)]. We also investigate the case where g is linear or sublinear and give an existence result for (P).
ER  -

NGUYEN, Phuoc-Tai. Semilinear elliptic equations with Hardy potential and subcritical source term. \textit{CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS}. Germany: Springer, 2017, roč.~56/2017, č.~2, s.~1-28. ISSN~0944-2669. Dostupné z: https://doi.org/10.1007/s00526-017-1144-6.

Přehled o publikaci