论文标题
在偶数上的共鸣Q曲对面问题的Leray-Schauder学位
Leray-Schauder degree for the resonant Q-curvature problem in even dimensions
论文作者
论文摘要
在本文中，使用巴赫里无穷大的临界点的理论，我们得出了一个确切的冒泡速率公式，用于在封闭的均匀依次的riemannian歧管上，谐振剂处方的Q展览方程。使用此过程，我们在正质量类型假设下得出了共鸣的Q展出问题的新生存结果。此外，我们在非平稳性假设下得出了具有规定的Q展出的共形度量的紧凑定理。此外，将冒泡的速率公式与构建一些爆炸的解决方案相结合，我们计算了在非偏差和Morse类型假设下的共振剂规定的Q-横向方程的Leray-Schauder度。
In this paper, using the theory of critical points at infinity of Bahri, we derive an exact bubbling rate formula for the resonant prescribed Q-curvature equation on closed even-dimensional Riemannian manifolds. Using this, we derive new existence results for the resonant prescribed Q-curvature problem under a positive mass type assumption. Moreover, we derive a compactness theorem for conformal metrics with prescribed Q-curvature under a non-degeneracy assumption. Furthermore, combining the bubbling rate formula with the construction of some blowing-up solutions, we compute the Leray-Schauder degree of the resonant prescribed Q-curvature equation under a non-degeneracy and Morse type assumption.
