论文标题
存在具有强大潜力的扰动临界差异方程的解决方案
Existence of solutions to a perturbed critical biharmonic equation with Hardy potential
论文作者
论文摘要
\在本文中，以下Biharmonic椭圆形问题\ begin {eqnarray*} \ begin {cases}Δ^2u-λ\ frac {| u |^{q-2} {| x | x |^s} | x |^s} = | u = \ dfrac {\ partial u} {\ partial n} = 0，＆x \ in \partialΩ\ end end {cases} \ end end {eqnarray*}。该方程的主要特征是它涉及一个耐寒术语和具有关键Sobolev指数的非线性。通过将与山通行证问题相关的能量功能的光纤图结合在一起，根据$ s $和$ q $的不同，可以证明一些正参数$λ$，该问题承认至少在非线性$ f（x，x，u）$的适当增长条件下至少有一个山间通道类型解决方案。
\ In this paper, the following biharmonic elliptic problem \begin{eqnarray*} \begin{cases} Δ^2u-λ\frac{|u|^{q-2}u}{|x|^s}=|u|^{2^{**}-2}u+ f(x,u), &x\inΩ,\\ u=\dfrac{\partial u}{\partial n}=0, &x\in\partialΩ\end{cases} \end{eqnarray*} is considered. The main feature of the equation is that it involves a Hardy term and a nonlinearity with critical Sobolev exponent. By combining a careful analysis of the fibering maps of the energy functional associated with the problem with the Mountain Pass Lemma, it is shown, for some positive parameter $λ$ depending on $s$ and $q$, that the problem admits at least one mountain pass type solution under appropriate growth conditions on the nonlinearity $f(x,u)$.
