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Entire large solutions to the k-Hessian equations with weights: Existence, uniqueness and asymptotic behavior
Journal of Mathematical Analysis and Applications ( IF 1.2 ) Pub Date : 2021-05-07 , DOI: 10.1016/j.jmaa.2021.125301 Haitao Wan , Yongxiu Shi , Xiaoyan Qiao
中文翻译:
具有权重的k -Hessian方程的整体大解:存在性,唯一性和渐近行为
更新日期:2021-05-11
Journal of Mathematical Analysis and Applications ( IF 1.2 ) Pub Date : 2021-05-07 , DOI: 10.1016/j.jmaa.2021.125301 Haitao Wan , Yongxiu Shi , Xiaoyan Qiao
This paper is concerned with the k-Hessian equation , where is positive in , is positive and increasing on with and satisfies the so-called Keller-Osserman condition. We first establish the existence of entire strictly k-convex large solutions to the equation. And then by constructing a new class of Karamata functions, we investigate the exact asymptotic behavior of entire strictly k-convex large solutions at infinity. Finally, we prove the uniqueness of solutions.
中文翻译:
具有权重的k -Hessian方程的整体大解:存在性,唯一性和渐近行为
本文涉及k -Hessian方程, 在哪里 是积极的 , 是积极的,并在增加 和 并满足所谓的Keller-Osserman条件。我们首先建立方程方程的整个完全k-凸大解的存在。然后,通过构造一类新的Karamata函数,我们研究了无穷大时整个严格k凸大解的精确渐近行为。最后,我们证明了解决方案的独特性。