RN 上一类p-Kirchhoff方程解的存在性研究
Study on Existence of Solutions for a p-Kirchhoff Elliptic Equation on RN
DOI: 10.12677/AAM.2021.1012453, PDF, HTML, 下载: 338  浏览: 2,488  科研立项经费支持
作者: 刘立华：盐城师范学院，江苏 盐城
关键词: p-Kirchhoff 椭圆方程 变分原理 (PS)序列 Pohozaev 恒等式；p-Kirchhoff Elliptic Equation； Variational Method； (PS) Sequence； Pohoz ev Identity
摘要: 本文研究如下一类p-Kirchhoff椭圆方程, (1) 非平凡弱解的存在性。其中 a, b, τ > 0, 1 < p < N, p < q < p(τ + 1) < p∗ 。基于变分原理，我们证得方程(1)至少存在一个非平凡解。本文的主要困难在千论证近似解序列的有界性和收敛性。
Abstract: In this paper, we study the existence of solutions for the following p-Kirchhoff elliptic equation , (1) with a, b, τ > 0, 1 < p < N, p < q < p(τ + 1) < p∗. By the variational methods, we prove that problem (1) admits at least one nontrivial solution. The main difficulty is to get a bounded (PS) sequence and extract a strong convergent subsequence from it.
文章引用：刘立华. RN 上一类p-Kirchhoff方程解的存在性研究[J]. 应用数学进展, 2021, 10(12): 4262-4271. https://doi.org/10.12677/AAM.2021.1012453

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