Publication details

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

Authors | |
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Year of publication | 2024 |

Type | Article in Periodical |

Magazine / Source | Journal of Geometric Analysis |

MU Faculty or unit | |

Citation | |

Web | https://link.springer.com/article/10.1007/s12220-024-01637-2 |

Doi | http://dx.doi.org/10.1007/s12220-024-01637-2 |

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

Description | 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) (-?_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 $M(t) = a + bt^{?-1}$, where $a, b > 0$ are given constants; $1<p<N$, $?_p = \text{div}(|\nabla u|^{p-2}\nabla u)$ 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 $?\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. |

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