AAM  >> Vol. 8 No. 8 (August 2019)

    带有非负局部项的p-Laplacian问题的径向正解
    Radial Positive Solutions of p-Laplacian Problem with Nonnegative Local Terms

  • 全文下载: PDF(585KB) HTML    PP.1418-1431   DOI: 10.12677/AAM.2019.88166  
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作者:  

曾 勇:广西大学,广西 南宁

关键词:
径向解上下解p-Laplacian问题Radial Solution Upper and Lower Solutions p-Laplacian Problem

摘要:

本文主要研究下面p-Laplacian问题径向解的存在性:

其中f 所m满足一定条件,我们主要通过上下解的方法来证明上述p-Laplacian问题有过原点的径 向解,首先我们做出原问题的辅助问题序列,然后通过求解此问题序列得出一个单调有界解序列, 从而可以得出当n → ∞ 时,存在一个u ∈ C1[0, 1) ∩ C[0, 1] 使得un → u,最后证明u 即为所求的 径向解,具体证明在第三部分给出。

In this paper, we mainly study the existence of radial solutions for the following p- Laplacian problem:

where f and m satisfy certain conditions. We prove that the above p-Laplacian problem has a radial solution through the origin mainly by means of upper and lower solutions. Firstly, we make the  auxiliary  problem  sequence  of  the  original  problem.  Then  we get a monotone bounded solution sequence by solving the problem sequence. Then we can get that when n tends to infinity, there exists a u, which makes this solution sequencetend to u. Finally, we prove that u is the radial solution of  the  original problem.  The concrete proof is given in the third part.


文章引用:
曾勇. 带有非负局部项的p-Laplacian问题的径向正解[J]. 应用数学进展, 2019, 8(8): 1418-1431. https://doi.org/10.12677/AAM.2019.88166

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