论文标题
加权双旋转方程的节点溶液，并具有关键的指数增长
Nodal solutions for the weighted biharmonic equation with critical exponential growth
论文作者
论文摘要
在本文中，我们处理$ b \ subset \ r^{4} $的对数加权第四阶椭圆方程式：$$ \ displayStyle（p_λ）~~δ（w（x）ΔU u} {\ partial n} \ quad \ mbox {on} \ quad \ partial b，$$ 鉴于亚当的类型不平等，假定非线性$ f $具有指数级别的临界增长。 通过使用Nehari集合中的约束最小化结合定量变形引理和度理论，我们证明了问题$（P_λ）$的淋巴结解决方案。
In this paper, we deal with the logarithmic weighted fourth order elliptic equation in the unit disk of $B\subset\R^{4}$: $$\displaystyle(P_λ)~~Δ(w(x) Δu) = λ f(x,u) \quad\mbox{ in }\quad B, \quad u=\frac{\partial u}{\partial n} \quad\mbox{ on } \quad\partial B,$$ where the nonlinearity $f$ is assumed to have exponential critical growth in view of Adam's type inequalities. By using the constrained minimization in Nehari set combined with the quantitative deformation lemma and degree theory, we prove the existence of nodal solutions to the problem $(P_λ)$ .
