Total positivity of Narayana matrices

We prove the total positivity of the Narayana triangles of type $A$ and type $B$, and thus affirmatively confirm a conjecture of Chen, Liang and Wang and a conjecture of Pan and Zeng. We also prove the strict total positivity of the Narayana squares of type $A$ and type $B$.     

A limit equation and bifurcation diagrams of semilinear elliptic equations with general supercritical growth

We study radial solutions of the semilinear elliptic equation

$\mathrm{\Delta }u+f(u)=0$

under rather general growth conditions on f. We construct a radial singular solution and study the intersection number between the singular solution and a regular solution. An application to bifurcation problems of elliptic Dirichlet problems is given. To this end, we derive a certain limit equation from the original equation at infinity, using a generalized similarity transformation. Through a generalized Cole–Hopf transformation, all the limit equations can be reduced into two typical cases, i.e., $\mathrm{\Delta }u+u^p=0$ and $\mathrm{\Delta }u+e^u=0$.     

矩阵方程X=Q+A~* (I_m⊕ X-C)~(-1) A的Hermitian正定解

研究了一类来源于插值理论的非线性矩阵方程.利用Kronecker积的性质以及Banach空间单调有界序列收敛原理证明了此类方程正定解的存在唯一性.另外也给出了此方程正定解的范围.     

关于一个新泛函的锥拉伸与锥压缩不动点定理及应用

引进了一个新的泛函,它包含了已有的很多类型的泛函.关于此泛函建立了一个泛函形式的锥拉伸与锥压缩不动点定理,并应用此定理研究了一类二阶两点边值问题,得到了该问题至少一个正解的存在性.     

一类带时滞的Watt型功能性反应的捕食系统的Hopf分支

研究一类具有时滞的Watt型功能性反应的捕食模型,通过分析正平衡点处的特征方程,讨论了该系统正平衡点的稳定性.应用Hopf分支理论,得到了该系统产生Hopf分支的条件.     

算子方程AX-XA*=B的正解与实正解

利用算子矩阵分块技巧和算子的广义逆,在A是幂等算子的情况下,给出了算子方程AX-XA＊=B有正解和有实正解的充要条件,并给出了正解和实正解的通式。     

一个直接解释逻辑斯蒂克3-周期映射分支的公式

In this paper we develop an algebraic formula in analyzing the bifurcation of the logistic map. Based on this formula, we give a new, short and rigorous proof for the period-3 bifurcation diagram of the logistic map. Therefore, we simplify the work in previous references and improve some insufficiently rigorous slight defects in them.     

Existence of positive solutions for nonlinear singular boundary value problem with p‐Laplacian

In this paper, we study the existence of positive solutions for the following Sturm–Liouville‐like four‐point singular boundary value problem (BVP) with p‐Laplacian where ?_p(s)=|s|^p?2 s, p>1, f is a lower semi‐continuous function. Using the fixed‐point theorem of cone expansion and compression of norm type, the existence of positive solution and infinitely many positive solutions for Sturm–Liouville‐like singular BVP with p‐Laplacian are obtained. Copyright © 2009 John Wiley & Sons, Ltd.     

POSITIVE SOLUTIONS FOR WEAKLY COUPLED NONLINEAR ELLIPTIC SYSTEMS

In this article,we consider the existence of positive solutions for weakly cou-pled nonlinear elliptic systems {-△u+u (1+a(x))|u| p-1 u+μ|u| α-2 u|v|β+λv in R~N,-△v+v=(1+bx))|v|p-1v+μ|u|α|v|β-2v+λu in R N.(0.1) To find nontrivial solutions,we first investigate autonomous systems.In this case,results of bifurcation from semi-trivial solutions are obtained by the implicit function theorem.Next,the existence of positive solutions of problem(0.1) is obtained by variational methods.     

Diophantine方程y~2=px(x~2+2)

设p是大于3的奇素数.本文证明了:当p≡5或7(mod 8)时,方程y~2=px(x~2+2)无正整数解(x,y);当p≡1(mod 8)时,该方程至多有1组解;当p≡3(mod 8)时,该方程至多有2组解.