论文标题
具有非线性卷积和类似锥形域的椭圆形不平等现象
Elliptic inequalities with nonlinear convolution and Hardy terms in cone-like domains
论文作者
论文摘要
我们研究不等式的$-ΔU-\fracμ{| x |^2} u \ geq（| x |^{ - α} * u^p） * u^p）u^q $ in nocked Cone $ \ Mathcal {C} c}_Ω $ s^{n-1} \ subset \ mathbb {r}^n，$ $ p，q，ρ> 0 $，$μ\ in \ mathbb {r} $和$ 0 \ leqα<n $。在上面，$ | x |^{ - α} * u^p $表示圆锥$ \ MATHCAL {C}_Ω^ρ$中的标准卷积运算符。我们讨论了$ n，p，q，α，μ$和$ω$的阳性解决方案的存在和不存在。还研究了对不平等系统的扩展。
We study the inequality $ -Δu - \fracμ{|x|^2} u \geq (|x|^{-α} * u^p)u^q$ in an unbounded cone $\mathcal{C}_Ω^ρ\subset \mathbb{R}^N$ ($N\geq 2$) generated by a subdomain $Ω$ of the unit sphere $S^{N-1}\subset \mathbb{R}^N,$ $p, q, ρ>0$, $μ\in \mathbb{R}$ and $0\leq α< N$. In the above, $|x|^{-α} * u^p$ denotes the standard convolution operator in the cone $\mathcal{C}_Ω^ρ$. We discuss the existence and nonexistence of positive solutions in terms of $N, p, q, α, μ$ and $Ω$. Extensions to systems of inequalities are also investigated.
