High Energy Solutions for p-Kirchhoff Elliptic Problems with
Hardy–Littlewood–Sobolev Nonlinearity

J 2024

High Energy Solutions for p-Kirchhoff Elliptic Problems with Hardy–Littlewood–Sobolev Nonlinearity

GOEL, Divya, Sushmita RAWAT and K. SREENADH

Basic information

Original name

High Energy Solutions for p-Kirchhoff Elliptic Problems with Hardy–Littlewood–Sobolev Nonlinearity

Authors

GOEL, Divya, Sushmita RAWAT (356 India, guarantor, belonging to the institution) and K. SREENADH

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/s12220-024-01637-2

UT WoS

001215445700001

Keywords in English

p-Laplacian; Hardy-Littlewood-Sobolev inequality; Pohožaev manifold; Radial solution; Kirchhoff equation

Abstract

V originále

This article deals with the study of the following Kirchhoff-Choquard problem: \begin{equation*} \begin{array}{cc} \displaystyle M\left(\, \int\limits_{\mathbb{R}^N}|\nabla u|^p\right) (-Δ_p) u + V(x)|u|^{p-2}u = \left(\, \int\limits_{\mathbb{R}^N}\frac{F(u)(y)}{|x-y|^μ}\,dy \right) f(u), \;\;\text{in} \; \mathbb{R}^N, u > 0, \;\; \text{in} \; \mathbb{R}^N, \end{array} \end{equation*} where $M$ models Kirchhoff-type nonlinear term of the form $M(t) = a + bt^{θ-1}$, where $a, b > 0$ are given constants; $1<p<N$, $Δ_p = \text{div}(|\nabla u|^{p-2}\nabla u)$ is the $p$-Laplacian operator; potential $V \in C^2(\mathbb{R}^N)$; $f$ is monotonic function with suitable growth conditions. We obtain the existence of a positive high energy solution for $θ\in \left[1, \frac{2N-μ}{N-p}\right) $ via the Pohožaev manifold and linking theorem. Apart from this, we also studied the radial symmetry of solutions of the associated limit problem.

Links

GA22-17403S, research and development project

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

Investor: Czech Science Foundation

Citovat

GOEL, Divya, Sushmita RAWAT and K. SREENADH. High Energy Solutions for p-Kirchhoff Elliptic Problems with Hardy–Littlewood–Sobolev Nonlinearity. Journal of Geometric Analysis. Springer, 2024, vol. 34, No 7, p. 1-36. ISSN 1050-6926. Available from: https://dx.doi.org/10.1007/s12220-024-01637-2.

@article{2402917,
   author = {Goel, Divya and Rawat, Sushmita and Sreenadh, K.},
   article_number = {7},
   doi = {http://dx.doi.org/10.1007/s12220-024-01637-2},
   keywords = {p-Laplacian; Hardy-Littlewood-Sobolev inequality; Pohožaev manifold; Radial solution; Kirchhoff equation},
   language = {eng},
   issn = {1050-6926},
   journal = {Journal of Geometric Analysis},
   title = {High Energy Solutions for p-Kirchhoff Elliptic Problems with Hardy–Littlewood–Sobolev Nonlinearity},
   url = {https://link.springer.com/article/10.1007/s12220-024-01637-2},
   volume = {34},
   year = {2024}
}

TY  - JOUR
ID  - 2402917
AU  - Goel, Divya - Rawat, Sushmita - Sreenadh, K.
PY  - 2024
TI  - High Energy Solutions for p-Kirchhoff Elliptic Problems with Hardy–Littlewood–Sobolev Nonlinearity
JF  - Journal of Geometric Analysis
VL  - 34
IS  - 7
SP  - 1-36
EP  - 1-36
PB  - Springer
SN  - 10506926
KW  - p-Laplacian
KW  - Hardy-Littlewood-Sobolev inequality
KW  - Pohožaev manifold
KW  - Radial solution
KW  - Kirchhoff equation
UR  - https://link.springer.com/article/10.1007/s12220-024-01637-2
N2  - This article deals with the study of the following Kirchhoff-Choquard problem: \begin{equation*} \begin{array}{cc} \displaystyle M\left(\, \int\limits_{\mathbb{R}^N}|\nabla u|^p\right) (-Δ_p) u + V(x)|u|^{p-2}u = \left(\, \int\limits_{\mathbb{R}^N}\frac{F(u)(y)}{|x-y|^μ}\,dy \right) f(u), \;\;\text{in} \; \mathbb{R}^N, u > 0, \;\; \text{in} \; \mathbb{R}^N, \end{array} \end{equation*} where $M$ models Kirchhoff-type nonlinear term of the form $M(t) = a + bt^{θ-1}$, where $a, b > 0$ are given constants; $1<p<N$, $Δ_p = \text{div}(|\nabla u|^{p-2}\nabla u)$ is the $p$-Laplacian operator; potential $V \in C^2(\mathbb{R}^N)$; $f$ is monotonic function with suitable growth conditions. We obtain the existence of a positive high energy solution for $θ\in \left[1, \frac{2N-μ}{N-p}\right) $ via the Pohožaev manifold and linking theorem. Apart from this, we also studied the radial symmetry of solutions of the associated limit problem.
ER  -

GOEL, Divya, Sushmita RAWAT and K. SREENADH. High Energy Solutions for p-Kirchhoff Elliptic Problems with Hardy–Littlewood–Sobolev Nonlinearity. \textit{Journal of Geometric Analysis}. Springer, 2024, vol.~34, No~7, p.~1-36. ISSN~1050-6926. Available from: https://dx.doi.org/10.1007/s12220-024-01637-2.

Detailed Information on Publication Record