在 $\mathbb{R}^{N}$ 中分数 $p(x,\cdot )$-Kirchhoff-type 方程的解决方案

IF 1.5 3区数学 Q1 MATHEMATICS

Journal of Inequalities and Applications Pub Date : 2024-09-19 DOI:10.1186/s13660-024-03204-3

Lili Wan

引用次数: 0

摘要

本文讨论了分式 $p(x,cdot)$ -Kirchhoff 型方程 $$ M\left (\int _{\mathbb{R}^{N}\times \mathbb{R}^{N}})\frac{1}{p(x,y)} \frac{|u(x)-u(y)|^{p(x,y)}}{|x-y|^{N+sp(x,y)}}dxdy\right )(-\Delta _{p(x,.)})^{s} u+|u|^{\bar{p}(x)-2}u=f(x,u).$$ 我们弱化了非线性项 f 的条件，并通过变分法得到了解的存在性和多重性，从而改进了之前的一些结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Solutions for fractional $p(x,\cdot )$-Kirchhoff-type equations in $\mathbb{R}^{N}$

In this paper, we discuss the fractional $p(x,\cdot )$ -Kirchhoff-type equations $$ M\left (\int _{\mathbb{R}^{N}\times \mathbb{R}^{N}} \frac{1}{p(x,y)} \frac{|u(x)-u(y)|^{p(x,y)}}{|x-y|^{N+sp(x,y)}}dxdy\right )(-\Delta _{p(x,.)})^{s} u+|u|^{\bar{p}(x)-2}u=f(x,u).$$ We weaken the conditions on the nonlinear term f and get the existence and multiplicity of solutions via variational methods, which improves some previous results.

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来源期刊

Journal of Inequalities and Applications 数学-数学

自引率

6.20%

发文量

136

期刊介绍： The aim of this journal is to provide a multi-disciplinary forum of discussion in mathematics and its applications in which the essentiality of inequalities is highlighted. This Journal accepts high quality articles containing original research results and survey articles of exceptional merit. Subject matters should be strongly related to inequalities, such as, but not restricted to, the following: inequalities in analysis, inequalities in approximation theory, inequalities in combinatorics, inequalities in economics, inequalities in geometry, inequalities in mechanics, inequalities in optimization, inequalities in stochastic analysis and applications.

在 \(\mathbb{R}^{N}\) 中分数 \(p(x,\cdot )\)-Kirchhoff-type 方程的解决方案

摘要