论文标题
涉及分数拉普拉斯操作员和具有指数临界增长的非线性的choquard对数方程
The Choquard logarithmic equation involving fractional Laplacian operator and a nonlinearity with exponential critical growth
论文作者
论文摘要
在目前的工作中，我们调查了Choquard GoogarithMic方程$（ - δ）^{\ frac {1} {2} {2}} u + au +λ（\ ln | \ cdot | \ cdot | \ cd ast |^2} {2} {2） $ a> 0 $，$λ> 0 $和一个非线性$ f $具有指数临界增长。我们证明了在山间通过水平上存在非平凡的解决方案，在指数批判性和亚临界生长下存在非平凡的基态解决方案。此外，当$ f $具有亚临界增长时，我们通过属理论保证了许多解决方案的存在。
In the present work we investigate the existence and multiplicity of nontrivial solutions for the Choquard Logarithmic equation $(-Δ)^{\frac{1}{2}} u + au + λ(\ln|\cdot|\ast |u|^{2})u = f(u) \textrm{ in } \mathbb{R}$, 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 under exponential critical and subcritical growth. Morever, when $ f $ has subcritical growth we guarantee the existence of infinitely many solutions, via genus theory.
