Sobolev hyperbola for the periodic parabolic Lane–Emden system
Sobolev hyperbola for the periodic parabolic Lane–Emden system
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DOI：
10.1088/1361-6544/ab5157
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发表时间：
2019-12
期刊：
影响因子：
1.7
通讯作者：
Haochuan Huang;Rui Huang;Jingxue Yin;Yang Cao
中科院分区：
文献类型：
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作者：
Haochuan Huang;Rui Huang;Jingxue Yin;Yang Cao
考虑周期抛物型Lane-Emden型系统，在有界域上具有周期系数，服从齐次Dirichlet边界条件。众所周知，对于椭圆组，在三维空间中，存在一条Sobolev双曲线，它刻画了非平凡解的存在和不存在。在这篇文章中，我们证明了这样的Sobolev双曲线对于周期Lane-Emden型系统周期解的存在也是关键的。此外，与椭圆型方程组不同，存在另一条曲线Pq=1，该曲线对于周期解的存在是唯一的。
Consider the periodic parabolic Lane–Emden type system , in a bounded domain of with periodic coefficients and , subject to homogeneous Dirichlet boundary condition. It is known that for the elliptic system , in the 3-dimensional (3D) space, there exists a Sobolev hyperbola , which characterizes the existence and nonexistence of nontrivial solutions. In this paper, we show that such a Sobolev hyperbola is also critical to the existence of periodic solutions for the periodic Lane–Emden type system. Moreover, different from the elliptic system, there exists another cure pq = 1, which is singular for the existence of periodic solutions.