论文标题
分数$ p $ -laplacian Choquard对数方程的存在和多重解决方案，涉及具有指数批判性和亚临界增长的非线性
Existence and multiplicity of solutions for the fractional $p$-Laplacian Choquard logarithmic equation involving a nonlinearity with exponential critical and subcritical growth
论文作者
论文摘要
在目前的工作中，我们获得了Choquard GoogarithMic方程$（ - δ）_ {p}^{s}^{s} u + | u |^{p-2} u +（\ ln | \ cdot | \ cdot | \ ast |^us | U | U | U | U | U | U | U | U |^f（f） } \mathbb{R}^N $ , where $ N=sp $, $ s\in (0, 1) $, $ p>2 $, $ a>0 $, $ λ>0 $ and $f: \mathbb{R}\rightarrow \mathbb{R} $ a continuous nonlinearity with exponential critical and subcritical growth.我们保证在山间通道水平上存在非平凡的解决方案，而在关键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，我们通过属理论证明了许多解决方案的存在。
In the present work we obtain the existence and multiplicity of nontrivial solutions for the Choquard logarithmic equation $(-Δ)_{p}^{s}u + |u|^{p-2}u + (\ln|\cdot|\ast |u|^{p})|u|^{p-2}u = f(u) \textrm{ \ in \ } \mathbb{R}^N $ , where $ N=sp $, $ s\in (0, 1) $, $ p>2 $, $ a>0 $, $ λ>0 $ and $f: \mathbb{R}\rightarrow \mathbb{R} $ a continuous nonlinearity with exponential critical and subcritical growth. We guarantee the existence of a nontrivial solution at the mountain pass level and a nontrivial ground state solution under critical and subcritical growth. Morever, when $ f $ has subcritical growth we prove the existence of infinitely many solutions, via genus theory.
