Schrödinger equations with singular potentials: linear and
nonlinear boundary value problems

J 2019

Schrödinger equations with singular potentials: linear and nonlinear boundary value problems

MARCUS, Moshe a Phuoc-Tai NGUYEN

Základní údaje

Originální název

Schrödinger equations with singular potentials: linear and nonlinear boundary value problems

Autoři

MARCUS, Moshe (376 Izrael, garant) a Phuoc-Tai NGUYEN (704 Vietnam, domácí)

Vydání

Mathematische Annalen, Germany, Springer Berlin Heidelberg, 2019, 0025-5831

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

Full Text

Impakt faktor

Impact factor: 1.136

Kód RIV

RIV/00216224:14310/19:00115008

Organizační jednotka

Přírodovědecká fakulta

DOI

http://dx.doi.org/10.1007/s00208-018-1734-4

UT WoS

000471203400012

Klíčová slova anglicky

Hardy potential; Martin kernel; moderate solutions; normalized boundary trace; critical exponent; good measures

Štítky

rivok

Příznaky

Mezinárodní význam, Recenzováno

Změněno: 21. 1. 2021 09:22, Mgr. Marie Šípková, DiS.

Anotace

V originále

Let RN (N3) be a C2 bounded domain and F< subset of> be a C2 submanifold with dimension 0kN-2. Denote F=(,F), V=F-2and CH(V) the Hardy constant relative to V in . We study positive solutions of equations (LE) -LVu=0 and (NE) -LVu+f(u)=0 in where LV=+V, CH(V) and fC(R) is an odd, monotone increasing function. We extend the notion of normalized boundary trace introduced in Marcus and Nguyen (Ann Inst H. Poincare (C) Non Linear Anal 34:69-88, 2015) and employ it to investigate the linear equation (LE). Using these results we obtain properties of moderate solutions of (NE). Finally we determine a criterion for subcriticality of points on relative to f and study b.v.p. for (NE). In particular we establish existence and stability results when the data is concentrated on the set of subcritical points.

Citovat

MARCUS, Moshe a Phuoc-Tai NGUYEN. Schrödinger equations with singular potentials: linear and nonlinear boundary value problems. Mathematische Annalen. Germany: Springer Berlin Heidelberg, 2019, roč. 374, 1-2, s. 361-394. ISSN 0025-5831. Dostupné z: https://dx.doi.org/10.1007/s00208-018-1734-4.

@article{1450177,
   author = {Marcus, Moshe and Nguyen, PhuocandTai},
   article_location = {Germany},
   article_number = {1-2},
   doi = {http://dx.doi.org/10.1007/s00208-018-1734-4},
   keywords = {Hardy potential; Martin kernel; moderate solutions; normalized boundary trace; critical exponent; good measures},
   language = {eng},
   issn = {0025-5831},
   journal = {Mathematische Annalen},
   title = {Schrödinger equations with singular potentials: linear and nonlinear boundary value problems},
   url = {https://link.springer.com/article/10.1007/s00208-018-1734-4},
   volume = {374},
   year = {2019}
}

TY  - JOUR
ID  - 1450177
AU  - Marcus, Moshe - Nguyen, Phuoc-Tai
PY  - 2019
TI  - Schrödinger equations with singular potentials: linear and nonlinear boundary value problems
JF  - Mathematische Annalen
VL  - 374
IS  - 1-2
SP  - 361-394
EP  - 361-394
PB  - Springer Berlin Heidelberg
SN  - 00255831
KW  - Hardy potential
KW  - Martin kernel
KW  - moderate solutions
KW  - normalized boundary trace
KW  - critical exponent
KW  - good measures
UR  - https://link.springer.com/article/10.1007/s00208-018-1734-4
L2  - https://link.springer.com/article/10.1007/s00208-018-1734-4
N2  - Let RN (N3) be a C2 bounded domain and F< subset of> be a C2 submanifold with dimension 0kN-2. Denote F=(,F), V=F-2and CH(V) the Hardy constant relative to V in . We study positive solutions of equations (LE) -LVu=0 and (NE) -LVu+f(u)=0 in where LV=+V, CH(V) and fC(R) is an odd, monotone increasing function. We extend the notion of normalized boundary trace introduced in Marcus and Nguyen (Ann Inst H. Poincare (C) Non Linear Anal 34:69-88, 2015) and employ it to investigate the linear equation (LE). Using these results we obtain properties of moderate solutions of (NE). Finally we determine a criterion for subcriticality of points on relative to f and study b.v.p. for (NE). In particular we establish existence and stability results when the data is concentrated on the set of subcritical points.
ER  -

MARCUS, Moshe a Phuoc-Tai NGUYEN. Schrödinger equations with singular potentials: linear and nonlinear boundary value problems. \textit{Mathematische Annalen}. Germany: Springer Berlin Heidelberg, 2019, roč.~374, 1-2, s.~361-394. ISSN~0025-5831. Dostupné z: https://dx.doi.org/10.1007/s00208-018-1734-4.

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