论文标题
$ n $ laplacian方程的解决方案的存在，不存在和渐近行为，涉及整个$ \ mathbb {r}^n $中的关键指数增长
Existence, nonexistence, and asymptotic behavior of solutions for $N$-Laplacian equations involving critical exponential growth in the whole $\mathbb{R}^N$
论文作者
论文摘要
在本文中，我们有兴趣研究一类椭圆形问题的解决方案的存在或不存在，涉及整个空间中的$ n $ laplacian运营商。所考虑的非线性涉及关键的特鲁丁 - 摩萨尔生长。我们的方法是非不同的，这样，我们可以解决文献中尚未包含的广泛问题。甚至$ w^{1，n}（\ Mathbb {r}^n）\ hookrightArrow l^\ infty（\ Mathbb {r}^n）$ fairing，我们建立了$ \ |U_λ\ | _ {l^\ | _ {l^\ infty（l^\ infty） \ | u \ | _ {w^{1，n}（\ mathbb {r}^n）}^θ$（对于某些$θ> 0 $），当$ u $是解决方案时。总而言之，我们探讨了一些渐近特性。
In this paper, we are interested in studying the existence or non-existence of solutions for a class of elliptic problems involving the $N$-Laplacian operator in the whole space. The nonlinearity considered involves critical Trudinger-Moser growth. Our approach is non-variational, and in this way, we can address a wide range of problems not yet contained in the literature. Even $W^{1,N}(\mathbb{R}^N)\hookrightarrow L^\infty(\mathbb{R}^N)$ failing, we establish $\|u_λ\|_{L^\infty(\mathbb{R}^N)} \leq C \|u\|_{W^{1,N}(\mathbb{R}^N)}^Θ$ (for some $Θ>0$), when $u$ is a solution. To conclude, we explore some asymptotic properties.
