Acta Mathematica Scientia (Series A)
Sponsored by　Wuhan Institute of Physics and
Mathematics, CAS, China
Edited by  Editorial Committee of Acta Mathematica
Scientia
Add: P. O. Box 71010, Wuhan 430071, China
Tel: 027-87199206(Series A & Series B)
086-27-87199087(Series B)
E-mail: actams@wipm.ac.cn
ISSN 1003-3998
CN 　42-1226/O
 The Solvability of Dual Minkowski Problem in $\mathbb{R}$2 Na Wei Acta mathematica scientia,Series A. 2019, 39 (6):  1314-1322.  Abstract ( 5 )   RICH HTML PDF(306KB) ( 8 )   In this paper, we study the existence of minimum of a constrained variational problem in the Sobolev space W1, 4($\mathbb{S}$). If ∫$_\mathbb{S}$g(θ)dθ>0, the minimum is a positive solution to the related Euler-Lagrange equation ${u^{\prime \prime }} + u = \frac{{g(\theta )}}{{u\left( {{u^2} + {u^{\prime 2}}} \right)}}, \theta \in {\rm{\mathbb{S}}}$ Based on this, we prove the solvability of the dual Minkowski problem in $\mathbb{R}$2 posed by Huang-Lutwak-Yang-Zhang[Acta Math, 2016, 216(2):325-338].
 Traveling Wave Solutions of the Generalized Hyperelastic-Rod Wave Equation Yongyi Gu,Wenjun Yuan,Yonghong Wu Acta mathematica scientia,Series A. 2019, 39 (6):  1342-1351.  Abstract ( 5 )   RICH HTML PDF(385KB) ( 21 )   In this paper, we study the generalized hyperelastic-rod wave equation. We changed the generalized hyperelastic-rod wave equation into a complex differential equation by using traveling wave transform and show that meromorphic solutions of the complex differential equation belong to the class W by the weak $\left\langle {h, k} \right\rangle$ condition and the Fuchs index. Furthermore, we find out all meromorphic solutions of the complex differential equation, then we obtain the traveling wave solutions of the generalized hyperelastic-rod wave equation. We can apply the idea of this study to some related mathematical physics equations.