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@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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