论文标题
亚临界第四阶系统解决方案的定性特性
Qualitative properties for solutions to subcritical fourth order systems
论文作者
论文摘要
我们证明了涉及总耦合系统的奇异解决方案的一些定性属性，这些系统涉及涉及总的 - pitaevskii-type非线性。我们的主要定理是[J. Serrin，Acta数学。 （1964）]，[P.-L。 Lions，J。微分方程（1980）]，[P。 Aviles，通讯。数学。物理。 （1987）]和[B. Gidas和J. Spruck，Comm。纯应用。数学。 （1981）]。在技术层面上，我们使用移动球方法将极限爆破解决方案分类为我们的系统。此外，采用渐近分析技术，我们表明这些解决方案确实是孤立奇异性附近的局部模型。我们还引入了新的第四阶非自治pohozaev函数，其单调性特性可改善由于[R. Soranzo，潜在的肛门。 （1997）]。
We prove some qualitative properties for singular solutions to a class of strongly coupled system involving a Gross--Pitaevskii-type nonlinearity. Our main theorems are vectorial fourth order counterparts of the classical results of [J. Serrin, Acta Math. (1964)], [P.-L. Lions, J. Differential Equations (1980)], [P. Aviles, Comm. Math. Phys. (1987)], and [B. Gidas and J. Spruck, Comm. Pure Appl. Math. (1981)]. On the technical level, we use the moving sphere method to classify the limit blow-up solutions to our system. Besides, applying asymptotic analysis techniques, we show that these solutions are indeed the local models near the isolated singularity. We also introduce a new fourth order nonautonomous Pohozaev functional, whose monotonicity properties yield improvement for the asymptotics results due to [R. Soranzo, Potential Anal. (1997)].
