Sign-changing solutions for a class of p-Laplacian Kirchhoff-type problem with logarithmic nonlinearity
"In this paper, we study the existence of ground state sign-changing solutions for following $p$-Laplacian Kirchhoff-type problem with logarithmic nonlinearity\begin{equation*} \left\{ \renewcommand{\arraystretch}{1.25} \begin{array}{ll} -(a+ b\int _{\Omega}|\nabla u|^{p}dx)\Delta_p u=|u|^{...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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AIMS Press
2020-02-01
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| Series: | AIMS Mathematics |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/10.3934/math.2020139/fulltext.html |
| _version_ | 1819205165806256128 |
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| author | Ya-Lei Li Da-Bin Wang Jin-Long Zhang |
| author_facet | Ya-Lei Li Da-Bin Wang Jin-Long Zhang |
| author_sort | Ya-Lei Li |
| collection | DOAJ |
| description | "In this paper, we study the existence of ground state sign-changing solutions for following $p$-Laplacian Kirchhoff-type problem with logarithmic nonlinearity\begin{equation*} \left\{ \renewcommand{\arraystretch}{1.25} \begin{array}{ll} -(a+ b\int _{\Omega}|\nabla u|^{p}dx)\Delta_p u=|u|^{q-2}u\ln u^2, ~x\in\Omega \\ u=0, ~\ x\in \partial\Omega, \end{array} \right.\end{equation*}where $\Omega\subset \mathbb{R}^{N}$ is a smooth bounded domain, $a, b>0$ are constant, 4 ≤ 2<em>p</em> < <em>q</em> < <em>p</em><sup>*</sup> and <em>N</em> > <em>p</em>. By using constraint variational method, topological degree theory and the quantitative deformation lemma, we prove the existence of ground state sign-changing solutions with precisely two nodal domains." |
| first_indexed | 2024-12-23T04:47:22Z |
| format | Article |
| id | doaj.art-f4040c9ae59f493bbe4b02c0ec645913 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-12-23T04:47:22Z |
| publishDate | 2020-02-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-f4040c9ae59f493bbe4b02c0ec6459132022-12-21T17:59:35ZengAIMS PressAIMS Mathematics2473-69882020-02-01532100211210.3934/math.2020139Sign-changing solutions for a class of p-Laplacian Kirchhoff-type problem with logarithmic nonlinearityYa-Lei Li0Da-Bin Wang1Jin-Long Zhang2Department of Applied Mathematics, Lanzhou University of Technology, Lanzhou, Gansu, 730050, P. R. ChinaDepartment of Applied Mathematics, Lanzhou University of Technology, Lanzhou, Gansu, 730050, P. R. ChinaDepartment of Applied Mathematics, Lanzhou University of Technology, Lanzhou, Gansu, 730050, P. R. China"In this paper, we study the existence of ground state sign-changing solutions for following $p$-Laplacian Kirchhoff-type problem with logarithmic nonlinearity\begin{equation*} \left\{ \renewcommand{\arraystretch}{1.25} \begin{array}{ll} -(a+ b\int _{\Omega}|\nabla u|^{p}dx)\Delta_p u=|u|^{q-2}u\ln u^2, ~x\in\Omega \\ u=0, ~\ x\in \partial\Omega, \end{array} \right.\end{equation*}where $\Omega\subset \mathbb{R}^{N}$ is a smooth bounded domain, $a, b>0$ are constant, 4 ≤ 2<em>p</em> < <em>q</em> < <em>p</em><sup>*</sup> and <em>N</em> > <em>p</em>. By using constraint variational method, topological degree theory and the quantitative deformation lemma, we prove the existence of ground state sign-changing solutions with precisely two nodal domains."https://www.aimspress.com/article/10.3934/math.2020139/fulltext.htmlp-laplacian kirchhoff-type equationnonlocal termvariation methodssign-changing solutions |
| spellingShingle | Ya-Lei Li Da-Bin Wang Jin-Long Zhang Sign-changing solutions for a class of p-Laplacian Kirchhoff-type problem with logarithmic nonlinearity AIMS Mathematics p-laplacian kirchhoff-type equation nonlocal term variation methods sign-changing solutions |
| title | Sign-changing solutions for a class of p-Laplacian Kirchhoff-type problem with logarithmic nonlinearity |
| title_full | Sign-changing solutions for a class of p-Laplacian Kirchhoff-type problem with logarithmic nonlinearity |
| title_fullStr | Sign-changing solutions for a class of p-Laplacian Kirchhoff-type problem with logarithmic nonlinearity |
| title_full_unstemmed | Sign-changing solutions for a class of p-Laplacian Kirchhoff-type problem with logarithmic nonlinearity |
| title_short | Sign-changing solutions for a class of p-Laplacian Kirchhoff-type problem with logarithmic nonlinearity |
| title_sort | sign changing solutions for a class of p laplacian kirchhoff type problem with logarithmic nonlinearity |
| topic | p-laplacian kirchhoff-type equation nonlocal term variation methods sign-changing solutions |
| url | https://www.aimspress.com/article/10.3934/math.2020139/fulltext.html |
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