| 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. |
Other formats:
BibTeX
LaTeX
RIS
@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.
|
