论文标题
在指数非线性生长下涉及连续电位的加权双旋转方程
Weighted biharmonic equations involving continous potentiel under exponential nonlinear growth
论文作者
论文摘要
我们在$ \ mathbb {r}^{4} $的单位球中处理一个加权的双臂问题。 鉴于亚当的类型不平等，假定非线性具有关键的指数增长。权重$ w（x）$是对数类型的，潜在的$ v $是$ \ overline {b} $上的积极连续功能。事实证明，山间通过定理对这个问题有非平凡的积极解决方案。我们通过证明浓度的紧凑性结果和合适的渐近条件来避免紧凑性丧失。
We deal with a weighted biharmonic problem in the unit ball of $\mathbb{R}^{4}$. The non-linearity is assumed to have critical exponential growth in view of Adam's type inequalities. The weight $w(x)$ is of logarithm type and the potential $V$ is a positive continuous function on $\overline{B}$. It is proved that there is a nontrivial positive weak solution to this problem by the mountain Pass Theorem. We avoid the loss of compactness by proving a concentration compactness result and by a suitable asymptotic condition.
