论文标题
解决非电力非线性的略微亚临界椭圆问题的解决方案
A solution to a slightly subcritical elliptic problem with non-power nonlinearity
论文作者
论文摘要
我们认为在有限的平滑域中具有非电力非线性的一个略微临界问题。对于这个问题，标准紧凑型嵌入不能像在功率类型非线性的情况下一样保证解决方案的存在。取而代之的是，我们使用ljapunov-schmidt还原方法来表明有一个阳性解决方案集中在罗宾函数的非分级临界点上。这是这种类型的广义略微临界问题的第一个存在结果。
We consider a slightly subcritical Dirichlet problem with a non-power nonlinearity in a bounded smooth domain. For this problem, standard compact embeddings cannot be used to guarantee the existence of solutions as in the case of power-type nonlinearities. Instead, we use a Ljapunov-Schmidt reduction method to show that there is a positive solution which concentrates at a non-degenerate critical point of the Robin function. This is the first existence result for this type of generalized slightly subcritical problems.
