# 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

DOI: 10.12677/AAM.2019.88166, PDF, HTML, 下载: 303  浏览: 388  科研立项经费支持

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.

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