P—adic超越连分数

本文借助于Ｔｈｕｅ－Ｓｉｅｇｅｌ－Ｒｏｔｈ定理的Ｐ－ａｄｉｃ类似，Ｐ－ａｄｉｃ代数数的有理逼近定理以及Ｐ－ａｄｉｃ简单连分数的一些性质给出了Ｐ－ａｄｉｃ数是超越数的两个充分条件。     

Banach空间上凸函数项级数

本文研究了Ｂａｎａｃｈ空间上凸函数项级数，给出了Ｍｏｒｅａｕ Ｒｏｃｋａｆｅｌａｒ定理的推广，做为它的应用，获得了Ｋｕｈｎ Ｔｕｃｋｅｒ定理的一个部分推广．     

复Banach空间上的Rouché定理

本文利用（广义）拓扑度的有关性质给出了一般复Ｂａｎａｃｈ空间上全纯映射的（广义）Ｒｏｕｃｈé定理．特别，在复平面上它以经典的Ｒｏｕｃｈé定理为特例．同时，它也给出了多复变全纯映射的相应定理及一些应用．     

一类R^2上奇异非线性双调和方程正整解

以Ｓｃｈａｕｄｅｒ Ｔｙｃｈｏｎｏｆｆ不动点定理为工具,建立了一类犚２ 上奇异非线性双调和方程正 的径向对称整体解的存在定理,并给出了解的有关性质．     

三角形广义正弦定理的统一形式

文 [1 ]、[2 ]分别类似于三角形的正弦定理 ,给出了一系列等式 ,并分别称之为“类正弦定理”和“广义正弦定理” .本文试就一般情形 ,利用正弦定理给出了三角形广义正弦定理 (或类正弦定理 )的统一形式 ,作为其特殊情况 ,我们得到了文 [1 ]、[2 ]中的主要结果 .定理　在△ＡＢＣ中 ,设Ａ′、Ｂ′、Ｃ′分别为边ＢＣ、ＣＡ、ＡＢ上的点 ,△ＡＢＣ的外接圆半径为Ｒ ,λ1、λ2 、λ3∈ [0 ,1 ],则有ＡＡ′ｓｉｎＢｓｉｎＣｃｓｃ(λ1Ａ +Ｂ) =ＢＢ′ｓｉｎＣｓｉｎＡｃｓｃ(λ2 Ｂ +Ｃ)= ＣＣ′ｓｉｎＡｓｉｎＢｃｓｃ(λ3Ｃ +Ａ) =2Ｒ (1 )或…     

一类R~2上奇异非线性双调和方程正整解

以 Ｓｃｈａｕｄｅｒ－Ｔｙｃｈｏｎｏｆｆ不动点定理为工具,建立了一类Ｒ２上奇异非线性双调和方程正的径向对称整体解的存在定理,并给出了解的有关性质.     

双层桥梁耦合系统的强迫振动

本文研究作为双层桥模型的梁方程耦合系统，利用Ｌｅｒａｙ－Ｓｃｈａｕｄｅｒ不动点定理，得到了一个关于这种系统的解的存在性定理，它类似于ＭｃＫｅｎｎａ和Ｗａｌｔｅｒ文２中关于吊桥方程的一个定理。     

R^2上带奇异性的非线性椭圆型方程的正整解

以Ｓｃｈａｕｄｅｒ－Ｔｙｃｈｏｎｏｆｆ不动点定理为工具,建立了一类在Ｒ＾２上带奇异性的非线性椭圆型方程正整解的存在性定理,并给出了解在无穷远的性质。     

广义蝴蝶定理的进一步拓广

广义蝴蝶定理的进一步拓广四川蓬溪中学田文宇在《数学通讯》１９９４年第４期上刊登了朱履乾同志的《广义蝴蝶定理》一文（简称文［１］），笔者对文［１］中所述广义蝴蝶定理作进一步拓广．定理设ｃ１，ｃ２，ｃ３为三条均过Ｍ、Ｎ、Ｔ、Ｓ四点的二次曲线，它们顺次与有...     

Banach空间中渐近正则的Lipschitz半群的不动点定理

本文首先定义了渐近正则的Ｌｉｐｓｃｈｉｔｚ半群的概念．其次，证明了ｐ一致凸Ｂａｎａｃｈ空间中渐近正则的Ｌｉｐｓｃｈｉｔｚ半群的不动点定理．同时也证明了具有正规结构系数的一致凸Ｅａｎａｃｈ空间中的渐近正则的Ｌｉｐｓｃｈｉｔｚ半群的一个新的不动点定理．     

Periodic Wave Solutions and Their Limits for the Modified Kd V–KP Equations

In this paper, we use the bifurcation method of dynamical systems to study the periodic wave solutions and their limits for the modified Kd V–KP equations. Some explicit periodic wave solutions are obtained. These solutions contain smooth periodic wave solutions and periodic blow-up solutions. Their limits contain solitary wave solutions, periodic wave solutions, kink wave solutions and unbounded solutions.     

Some new nonlinear wave solutions and their convergence for the (2+1)‐dimensional Broer–Kau–Kupershmidt equation

We use the bifurcation method of dynamical systems to study the (2+1)‐dimensional Broer–Kau–Kupershmidt equation. We obtain some new nonlinear wave solutions, which contain solitary wave solutions, blow‐up wave solutions, periodic smooth wave solutions, periodic blow‐up wave solutions, and kink wave solutions. When the initial value vary, we also show the convergence of certain solutions, such as the solitary wave solutions converge to the kink wave solutions and the periodic blow‐up wave solutions converge to the solitary wave solutions. Copyright © 2014 John Wiley & Sons, Ltd.     

关于运输问题最优解的进一步讨论

首先给出了运输问题最优解的相关概念,将最优解扩展到广义范畴,提出狭义多重最优解和广义多重最优解的概念及其区别.然后给出了惟一最优解、多重最优解、广义有限多重最优解、广义无限多重最优解的判定定理及其证明过程.最后推导出了狭义有限多重最优解个数下限和广义有限多重最优解个数上限的计算公式,并举例验证了结论的正确性.     

Qualitative analysis and explicit traveling wave solutions for the Davey–Stewartson equation

In this paper, we use the bifurcation method of dynamical systems to study the traveling wave solutions for the Davey–Stewartson equation. A number of traveling wave solutions are obtained. Those solutions contain explicit periodic wave solutions, periodic blow‐up wave solutions, unbounded wave solutions, kink profile solitary wave solutions, and solitary wave solutions. Relations of the traveling wave solutions are given. Some previous results are extended. Copyright © 2013 John Wiley & Sons, Ltd.     

Solutions of the generalized Lennard-Jones system

In this paper, we study solution structures of the following generalized Lennard-Jones system in R~n,x=(-α/|x|~(α+2)+β/|x|~(β+2))x,with 0 α β. Considering periodic solutions with zero angular momentum, we prove that the corresponding problem degenerates to 1-dimensional and possesses infinitely many periodic solutions which must be oscillating line solutions or constant solutions. Considering solutions with non-zero angular momentum, we compute Morse indices of the circular solutions first, and then apply the mountain pass theorem to show the existence of non-circular solutions with non-zero topological degrees. We further prove that besides circular solutions the system possesses in fact countably many periodic solutions with arbitrarily large topological degree, infinitely many quasi-periodic solutions, and infinitely many asymptotic solutions.     

Several classes of exact solutions to the 1 + 1 Born–Infeld equation

We obtain closed-form exact solutions to the 1 + 1 Born–Infeld equation arising in nonlinear electrodynamics. In particular, we obtain general traveling wave solutions of one wave variable, solutions of two wave variables, similarity solutions, multiplicatively separable solutions, and additively separable solutions. Then, putting the Born–Infeld model into correspondence with the minimal surface equation using a Wick rotation, we are able to construct complex helicoid solutions, transformed catenoid solutions, and complex analogues of Scherk’s first and second surfaces. Some of the obtained solutions are new, whereas others are generalizations of solutions in the literature. These exact solutions demonstrate the fact that solutions to the Born–Infeld model can exhibit a variety of behaviors. Exploiting the integrability of the Born–Infeld equation, the solutions are constructed elegantly, without the need for complicated analytical algorithms.     

小展弦比波的Green-Naghdi渐进模型的行波解

本文研究了小展弦比波的Green-Naghdi渐进模型. 利用平面自治系统的稳定性分析方法, 在不同的参数条件下, 讨论了它的行波系统的分岔并且给出了对应的相图, 得到了光滑周期波解, 广义扭波解, 广义反扭波解, 广义紧波解, 周期尖波解, 孤波解和孤立尖波解的精确表达式. 进一步, 通过数学软件Maple模拟了这些解.     

Symbolic computation of exact solutions for a nonlinear evolution equation

In this paper, by means of the Jacobi elliptic function method, exact double periodic wave solutions and solitary wave solutions of a nonlinear evolution equation are presented. It can be shown that not only the obtained solitary wave solutions have the property of loop-shaped, cusp-shaped and hump-shaped for different values of parameters, but also different types of double periodic wave solutions are possible, namely periodic loop-shaped wave solutions, periodic hump-shaped wave solutions or periodic cusp-shaped wave solutions. Furthermore, periodic loop-shaped wave solutions will be degenerated to loop-shaped solitary wave solutions for the same values of parameters. So do cusp-shaped solutions and hump-shaped solutions. All these solutions are new and first reported here.     

A series of abundant exact travelling wave solutions for a modified generalized Vakhnenko equation using auxiliary equation method

In this paper, a series of abundant exact travelling wave solutions is established for a modified generalized Vakhnenko equation by using auxiliary equation method. These solutions can be expressed by Jacobi elliptic function. When Jacobi elliptic functions modulus m→1 or 0, the travelling wave solutions degenerate to four types of solutions, namely, the soliton solutions, the hyperbolic function solutions, the trigonometric function solutions, constant solutions.     

Scalarization and optimality conditions for vector equilibrium problems

In this paper, we investigated vector equilibrium problems and gave the scalarization results for weakly efficient solutions, Henig efficient solutions, and globally efficient solutions to the vector equilibrium problems without the convexity assumption. Using nonsmooth analysis and the scalarization results, we provided the necessary conditions for weakly efficient solutions, Henig efficient solutions, globally efficient solutions, and superefficient solutions to vector equilibrium problems. By the assumption of convexity, we gave sufficient conditions for those solutions. As applications, we gave the necessary and sufficient conditions for corresponding solutions to vector variational inequalities and vector optimization problems.