论文标题
用于亚临界第六阶方程的积极奇异解决方案的渐近学
Asymptotics for positive singular solutions to subcritical sixth order equations
论文作者
论文摘要
我们将正奇异溶液的局部渐近行为分类为刺破球上的一类亚临界六阶方程。最初，使用积分移动球技术的版本，我们证明解决方案是渐近径向对称的解决方案，相对于原点。我们将我们的方法分为某些涉及非线性增长的情况。通常，我们使用emden的变量变化将我们的问题转化为圆柱体。在较低的临界制度中，这还不够，因此，我们需要引入变化的新概念。困难是该坐标系中的圆柱形PDE是非自主的。但是，我们定义了相关的非自治pohozaev功能，可以证明是渐近单调的。此外，我们还显示了这两个功能的先验估计值，从中我们提取紧凑型特性。使用这些成分，我们可以执行渐近分析技术以证明我们的主要结果。
We classify the local asymptotic behavior of positive singular solutions to a class of subcritical sixth order equations on the punctured ball. Initially, using a version of the integral moving spheres technique, we prove that solutions are asymptotically radially symmetric solutions with respect to the origin. We divide our approach into some cases concerning the growth of nonlinearity. In general, we use an Emden--Fowler change of variables to translate our problem to a cylinder. In the lower critical regime, this is not enough, thus, we need to introduce a new notion of change of variables. The difficulty is that the cylindrical PDE in this coordinate system is nonautonomous. Nonetheless, we define an associated nonautonomous Pohozaev functional, which can be proved to be asymptotically monotone. In addition, we show a priori estimates for these two functionals, from which we extract compactness properties. With this ingredients, we can perform an asymptotic analysis technique to prove our main result.
