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

作　　者：曾勇 

机构地区：[1]广西大学,广西南宁

出　　处：《应用数学进展》2019年第8期1418-1431,共14页Advances in Applied Mathematics

基　　金：广西大学科研基金项目(XGZ160535).

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.

关 键 词：径向解 上下解 p-Laplacian问题 

分 类 号：O1[理学—数学]