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。
Abstract:
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.