摘要: 本文研究如下一类p-Kirchhoff椭圆方程
![](https://image.hanspub.org/IMAGE/Edit_2f897a53-a18e-42b6-bd51-ec586ed7cf01.png)
, (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
![](https://image.hanspub.org/IMAGE/Edit_f2a624a7-acb9-49c7-919a-9d689f144887.png)
, (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.