Quasilinear Schrödinger equations with Stein-Weiss type
convolution and critical exponential nonlinearity in R^N

J 2024

Quasilinear Schrödinger equations with Stein-Weiss type convolution and critical exponential nonlinearity in R^N

BISWAS, Reshmi, Sarika GOYAL and K. SREENADH

Basic information

Original name

Quasilinear Schrödinger equations with Stein-Weiss type convolution and critical exponential nonlinearity in R^N

Authors

BISWAS, Reshmi (356 India, belonging to the institution), Sarika GOYAL and K. SREENADH (guarantor)

Edition

Journal of Geometric Analysis, Springer, 2024, 1050-6926

Other information

Language

English

Type of outcome

Článek v odborném periodiku

Field of Study

10101 Pure mathematics

Country of publisher

United States of America

Confidentiality degree

není předmětem státního či obchodního tajemství

References:

URL

Impact factor

Impact factor: 1.100 in 2022

Organization unit

Faculty of Science

DOI

http://dx.doi.org/10.1007/s12220-023-01505-5

UT WoS

001134164400002

Keywords in English

Quasilinear Schrödinger equation; N-Laplacian; Stein-Weiss type convolution; Trudinger-Moser inequality; Critical exponent

Abstract

V originále

In this article, we investigate the existence of the positive solutions to the following class of quasilinear {Schr\"odinger} equations involving Stein-Weiss type convolution \begin{align*} -\Delta_N u -\Delta_N (u^{2})u +V(x)|u|^{N-2}u= \left(\int_{\mathbb R^N}\frac{F(y,u)}{|y|^\beta|x-y|^{\mu}}~dy\right)\frac{f(x,u)}{|x|^\beta} \;\; \text{ in}\; \mathbb R^N, \end{align*} where $N\geq 2,\,$ $0<\mu<N,\, \beta\geq 0,$ and $2\beta+\mu\leq N.$ The potential $V:\mathbb R^N\to \mathbb R$ is a continuous function satisfying $0<V_0\leq V(x)$ for all $x\in \mathbb R^N$ and some appropriate assumptions. The nonlinearity $f:\mathbb R^N\times \mathbb R\to \mathbb R$ is a continuous function with critical exponential growth in the sense of the Trudinger-Moser inequality and $F(x,s)=\int_{0}^s f(x,t)dt$ is the primitive of $f$.

Citovat

BISWAS, Reshmi, Sarika GOYAL and K. SREENADH. Quasilinear Schrödinger equations with Stein-Weiss type convolution and critical exponential nonlinearity in R^N. Journal of Geometric Analysis. Springer, 2024, vol. 34, No 2, p. 1-52. ISSN 1050-6926. Available from: https://dx.doi.org/10.1007/s12220-023-01505-5.

@article{2367057,
   author = {Biswas, Reshmi and Goyal, Sarika and Sreenadh, K.},
   article_number = {2},
   doi = {http://dx.doi.org/10.1007/s12220-023-01505-5},
   keywords = {Quasilinear Schrödinger equation; N-Laplacian; Stein-Weiss type convolution; Trudinger-Moser inequality; Critical exponent},
   language = {eng},
   issn = {1050-6926},
   journal = {Journal of Geometric Analysis},
   title = {Quasilinear Schrödinger equations with Stein-Weiss type convolution and critical exponential nonlinearity in R^N},
   url = {https://link.springer.com/article/10.1007/s12220-023-01505-5},
   volume = {34},
   year = {2024}
}

TY  - JOUR
ID  - 2367057
AU  - Biswas, Reshmi - Goyal, Sarika - Sreenadh, K.
PY  - 2024
TI  - Quasilinear Schrödinger equations with Stein-Weiss type convolution and critical exponential nonlinearity in R^N
JF  - Journal of Geometric Analysis
VL  - 34
IS  - 2
SP  - 1-52
EP  - 1-52
PB  - Springer
SN  - 10506926
KW  - Quasilinear Schrödinger equation
KW  - N-Laplacian
KW  - Stein-Weiss type convolution
KW  - Trudinger-Moser inequality
KW  - Critical exponent
UR  - https://link.springer.com/article/10.1007/s12220-023-01505-5
N2  - In this article, we investigate the existence of the positive solutions to the following class of quasilinear {Schr\"odinger} equations involving Stein-Weiss type convolution \begin{align*} -\Delta_N u -\Delta_N (u^{2})u +V(x)|u|^{N-2}u= \left(\int_{\mathbb R^N}\frac{F(y,u)}{|y|^\beta|x-y|^{\mu}}~dy\right)\frac{f(x,u)}{|x|^\beta} \;\; \text{ in}\; \mathbb R^N, \end{align*} where $N\geq 2,\,$ $0<\mu<N,\, \beta\geq 0,$ and $2\beta+\mu\leq N.$ The potential $V:\mathbb R^N\to \mathbb R$ is a continuous function satisfying $0<V_0\leq V(x)$ for all $x\in \mathbb R^N$ and some appropriate assumptions. The nonlinearity $f:\mathbb R^N\times \mathbb R\to \mathbb R$ is a continuous function with critical exponential growth in the sense of the Trudinger-Moser inequality and $F(x,s)=\int_{0}^s f(x,t)dt$ is the primitive of $f$.
ER  -

BISWAS, Reshmi, Sarika GOYAL and K. SREENADH. Quasilinear Schrödinger equations with Stein-Weiss type convolution and critical exponential nonlinearity in R\^{}N. \textit{Journal of Geometric Analysis}. Springer, 2024, vol.~34, No~2, p.~1-52. ISSN~1050-6926. Available from: https://dx.doi.org/10.1007/s12220-023-01505-5.

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