论文标题
加权双马型问题的基态解决方案，涉及非线性指数增长
Ground state solutions for weighted biharmonic problem involving non linear exponential growth
论文作者
论文摘要
在本文中，我们研究以下问题$$δ（w（x）Δu）= \ f（x，x，u）\ quad \ mbox {in} 其中$ b $是$ \ mathbb {r}^{4} $的单位球和$ w（x）$奇异的对数类型。反应源$ f（x，u）$是$ x $的径向功能，鉴于亚当斯类型的指数不平等，至关重要。通过使用尼哈里集合中的约束最小化以及定量变形引理和程度理论结果，证明了存在结果。
In this article, we study the following problem $$Δ(w(x)Δu) = \ f(x,u) \quad\mbox{ in }\quad B, \quad u=\frac{\partial u}{\partial n}=0 \quad\mbox{ on } \quad\partial B,$$ where $B$ is the unit ball of $\mathbb{R}^{4}$ and $ w(x)$ a singular weight of logarithm type. The reaction source $f(x,u)$ is a radial function with respect to $x$ and it is critical in view of exponential inequality of Adams' type. The existence result is proved by using the constrained minimization in Nehari set coupled with the quantitative deformation lemma and degree theory results.
