$G$-invariant positive solutions for a quasilinear Schrödinger equation
$G$-invariant positive solutions for a quasilinear Schrödinger equation
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DOI：
10.57262/ade/1355854310
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发表时间：
2011-03
影响因子：
1.4
通讯作者：
Shinji Adachi;Tatsuya Watanabe
中科院分区：
文献类型：
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作者：
Shinji Adachi;Tatsuya Watanabe
本文讨论了一个拟线性椭圆型方程：− a-u + a（x）-a-u（|u| α）|u|在R中，α−2u = h（u），其中α > 1且N ≥ 1。利用变分方法证明了在适当的条件下，在a（x）和h上，上述方程至少存在一个正解。特别地，我们对有限群作用G下a（x）不变的情形很感兴趣.
We are concerned with a quasilinear elliptic equation of the form: −∆u+ a(x)u−∆(|u|α)|u|α−2u = h(u) in R , where α > 1 and N ≥ 1. By using variational approaches, we prove the existence of at least one positive solution of the above equation under suitable conditions on a(x) and h. Especially, we are interested in the situation that a(x) is invariant under the finite group action G.