论文标题
指数非线性生长下的第四阶加权椭圆问题
Fourth order weighted elliptic problem under exponential nonlinear growth
论文作者
论文摘要
我们在$ \ mathbb {r}^{4} $的单位球中处理非线性加权Biharmonic问题。重量是对数类型的。鉴于Adam在加权Sobolev空间中的不等式$ W^{2,2} _ {0}（B，W）$中，非线性至关重要。我们通过临界点理论证明了非琐碎解决方案的存在。主要困难是由于非线性项$ f $的临界指数增长而导致紧凑性的丧失。我们给出了新的生长条件，并指出了它对检查宫殿的紧凑条件的重要性。
We deal with nonlinear weighted biharmonic problem in the unit ball of $\mathbb{R}^{4}$. The weight is of logarithm type. The nonlinearity is critical in view of Adam's inequalities in the weighted Sobolev space $W^{2,2}_{0}(B,w)$. We prove the existence of non trivial solutions via the critical point theory. The main difficulty is the loss of compactness due to the critical exponential growth of the nonlinear term $f$. We give a new growth condition and we point out its importance for checking the Palais-Smale compactness condition.
