Existence of positive radial solutions to a p-Laplacian Kirchhoff type problem on the exterior of a ball

IF 1 Q1 MATHEMATICS Opuscula Mathematica Pub Date : 2023-01-01 DOI:10.7494/opmath.2023.43.1.47
J. Graef, Doudja Hebboul, T. Moussaoui
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引用次数: 1

Abstract

In this paper the authors study the existence of positive radial solutions to the Kirchhoff type problem involving the \(p\)-Laplacian \[-\Big(a+b\int_{\Omega_e}|\nabla u|^p dx\Big)\Delta_p u=\lambda f\left(|x|,u\right),\ x\in \Omega_e,\quad u=0\ \text{on} \ \partial\Omega_e,\] where \(\lambda \gt 0\) is a parameter, \(\Omega_e = \lbrace x\in\mathbb{R}^N : |x|\gt r_0\rbrace\), \(r_0\gt 0\), \(N \gt p \gt 1\), \(\Delta_p\) is the \(p\)-Laplacian operator, and \(f\in C(\left[ r_0, +\infty\right)\times\left[0,+\infty\right),\mathbb{R})\) is a non-decreasing function with respect to its second variable. By using the Mountain Pass Theorem, they prove the existence of positive radial solutions for small values of \(\lambda\).
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球外p- laplace Kirchhoff型问题径向正解的存在性
本文研究了涉及\(p\) -Laplacian \[-\Big(a+b\int_{\Omega_e}|\nabla u|^p dx\Big)\Delta_p u=\lambda f\left(|x|,u\right),\ x\in \Omega_e,\quad u=0\ \text{on} \ \partial\Omega_e,\]的Kirchhoff型问题的正径向解的存在性,其中\(\lambda \gt 0\)是参数,\(\Omega_e = \lbrace x\in\mathbb{R}^N : |x|\gt r_0\rbrace\), \(r_0\gt 0\), \(N \gt p \gt 1\), \(\Delta_p\)是\(p\) -Laplacian算子,\(f\in C(\left[ r_0, +\infty\right)\times\left[0,+\infty\right),\mathbb{R})\)是关于其第二变量的非递减函数。利用山口定理,证明了\(\lambda\)小值时径向正解的存在性。
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来源期刊
Opuscula Mathematica
Opuscula Mathematica MATHEMATICS-
CiteScore
1.70
自引率
20.00%
发文量
30
审稿时长
22 weeks
期刊最新文献
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