Boundary value problems for semilinear Schrödinger equations
with singular potentials and measure data

J 2024

Boundary value problems for semilinear Schrödinger equations with singular potentials and measure data

BHAKTA, Mousomi, Moshe MARCUS and Phuoc-Tai NGUYEN

Basic information

Original name

Boundary value problems for semilinear Schrödinger equations with singular potentials and measure data

Authors

BHAKTA, Mousomi, Moshe MARCUS (guarantor) and Phuoc-Tai NGUYEN (704 Viet Nam, belonging to the institution)

Edition

Mathematische Annalen, Germany, Springer Berlin Heidelberg, 2024, 0025-5831

Other information

Language

English

Type of outcome

Článek v odborném periodiku

Field of Study

10101 Pure mathematics

Country of publisher

Germany

Confidentiality degree

není předmětem státního či obchodního tajemství

References:

URL

Impact factor

Impact factor: 1.400 in 2022

Organization unit

Faculty of Science

DOI

http://dx.doi.org/10.1007/s00208-023-02764-x

UT WoS

001118338300001

Keywords in English

Semilinear elliptic equations; Singular elliptic equations; Schrödinger operator; Schrödinger equation

Abstract

V originále

We study boundary value problems with measure data in smooth bounded domains Omega, for semilinear equations. Specifically we consider problems of the form - L(V)u + f (u) = tau in Omega and tr(V)u = nu on partial derivative Omega, where L-V = Delta + V, f. is an element of C(R) is monotone increasingwith f (0) = 0 and tr V u denotes themeasure boundary trace of u associated with L-V. The potential V is an element of C-1(Omega) typically blows up at a set F subset of partial derivative Omega as dist (x, F)(-2). In general the above boundary value problem may not have a solution. We are interested in questions related to the concept of 'reduced measures', introduced in Brezis et al. (Ann Math Stud 163:55-109, 20072007) for V = 0. Our results extend results of [4] and Brezis and Ponce (J Funct Anal 229(1):95-120, 2005) and apply to a larger class of nonlinear terms f. In the case of signed measures, some of the present results are new even for V = 0.

Links

GA22-17403S, research and development project

Name: Nelineární Schrödingerovy rovnice a systémy se singulárním potenciálem (Acronym: NSESSP)

Investor: Czech Science Foundation

Citovat

BHAKTA, Mousomi, Moshe MARCUS and Phuoc-Tai NGUYEN. Boundary value problems for semilinear Schrödinger equations with singular potentials and measure data. Mathematische Annalen. Germany: Springer Berlin Heidelberg, 2024, vol. 390, No 1, p. 351-379. ISSN 0025-5831. Available from: https://dx.doi.org/10.1007/s00208-023-02764-x.

@article{2441258,
   author = {Bhakta, Mousomi and Marcus, Moshe and Nguyen, PhuocandTai},
   article_location = {Germany},
   article_number = {1},
   doi = {http://dx.doi.org/10.1007/s00208-023-02764-x},
   keywords = {Semilinear elliptic equations; Singular elliptic equations; Schrödinger operator; Schrödinger equation},
   language = {eng},
   issn = {0025-5831},
   journal = {Mathematische Annalen},
   title = {Boundary value problems for semilinear Schrödinger equations with singular potentials and measure data},
   url = {https://link.springer.com/article/10.1007/s00208-023-02764-x},
   volume = {390},
   year = {2024}
}

TY  - JOUR
ID  - 2441258
AU  - Bhakta, Mousomi - Marcus, Moshe - Nguyen, Phuoc-Tai
PY  - 2024
TI  - Boundary value problems for semilinear Schrödinger equations with singular potentials and measure data
JF  - Mathematische Annalen
VL  - 390
IS  - 1
SP  - 351-379
EP  - 351-379
PB  - Springer Berlin Heidelberg
SN  - 00255831
KW  - Semilinear elliptic equations
KW  - Singular elliptic equations
KW  - Schrödinger operator
KW  - Schrödinger equation
UR  - https://link.springer.com/article/10.1007/s00208-023-02764-x
N2  - We study boundary value problems with measure data in smooth bounded domains Omega, for semilinear equations. Specifically we consider problems of the form - L(V)u + f (u) = tau in Omega and tr(V)u = nu on partial derivative Omega, where L-V = Delta + V, f. is an element of C(R) is monotone increasingwith f (0) = 0 and tr V u denotes themeasure boundary trace of u associated with L-V. The potential V is an element of C-1(Omega) typically blows up at a set F subset of partial derivative Omega as dist (x, F)(-2). In general the above boundary value problem may not have a solution. We are interested in questions related to the concept of 'reduced measures', introduced in Brezis et al. (Ann Math Stud 163:55-109, 20072007) for V = 0. Our results extend results of [4] and Brezis and Ponce (J Funct Anal 229(1):95-120, 2005) and apply to a larger class of nonlinear terms f. In the case of signed measures, some of the present results are new even for V = 0.
ER  -

BHAKTA, Mousomi, Moshe MARCUS and Phuoc-Tai NGUYEN. Boundary value problems for semilinear Schrödinger equations with singular potentials and measure data. \textit{Mathematische Annalen}. Germany: Springer Berlin Heidelberg, 2024, vol.~390, No~1, p.~351-379. ISSN~0025-5831. Available from: https://dx.doi.org/10.1007/s00208-023-02764-x.

Detailed Information on Publication Record