论文标题
涉及指数增长的非线性的choquard对数方程
The Choquard logarithmic equation involving a nonlinearity with exponential growth
论文作者
论文摘要
在目前的工作中，我们关注的是choquard对数方程$-ΔU + au + au +λ（\ ln | \ cdot | \ ast | u |^{2}）我们证明了在山间通过水平和非平凡基态解决方案的非平凡溶液的存在。此外，考虑到$ O（2）$的亚组，我们在对称设置下提供了这些结果。
In the present work we are concerned with the Choquard Logarithmic equation $-Δu + au + λ(\ln|\cdot|\ast |u|^{2})u = f(u)$ in $\mathbb{R}^2$, for $ a>0 $, $ λ>0 $ and a nonlinearity $f$ with exponential critical growth. We prove the existence of a nontrivial solution at the mountain pass level and a nontrivial ground state solution. Also, we provide these results under a symmetric setting, taking into account subgroups of $ O(2) $.
