二阶常微分方程及Thomas—Fermi方程的边值问题

本文利用上、下解方法推广了Ｍ．Ｌｅｅｓ关于半线性边值问题的结果，给出了另一类边值问题解的存在唯一性的一个充分条件；并利用所得的结果证明了Ｔｈｏｍａｓ－Ｆｅｒｍｉ方程的边值问题解的存在唯一性，从而推广了Ｃ．Ｄ．Ｌｕｎｉｎｇ的结果。     

Thomas－Fermi方程的孤立中性原子型边值问题

本文利用构造上、下解方法，研究奇异方程、（ｔ）Ｘ＇＇＝ｆ（ｔ，ｘ）的极限边值问题解的存在唯一性，证明了Ｔｈｏｍｓ－Ｆｅｒｍｉ方程对应于孤立中性原子型边值问题有唯一解，所得结果推广了Ａ．Ｍａｍｂｒｉａｎｉ定理     

Thomas—Fermi方程的孤立中性原子型边值问题

本文利用构造上、下解方法、研究奇异方程ψ（ｔ）ｘ‘’＝ｆ（ｔ，ｘ）的极限边值问题解的存在唯一性，证明了Ｔｈｏｍｓ－Ｆｅｒｍｉ方程对应于孤立中性原子型边值问题有唯一解，所得结果推广了Ａ．Ｍａｍｂｒｉａｎｉ定理。     

一类半线性方程周期边值问题

本文运用整体反函数理论证明了一类半线性方程边值问题周期解的存在唯一性，推广和改进了已有的一些结果．     

线性Schrdinger方程的初边值问题(英文)

本文证明了非线性 Ｓｃｈｒｏｄｉｎｇｅｒ方程的初边值问题的 Ｈｓ－解（１＜ ｓ ≤ ２）的存在唯一性结果．     

n阶RFDE边值问题解的存在性和唯一性

利用不动点原理研究n阶RFDE边值问题解的存在性和唯一性，得到了一些新的结果．     

吸引盆在二阶抛物线边值问题解存在唯一性中的应用

本文研究了二阶抛物线边值问题解的存在唯一性的问题.利用吸引盆的方法和全局同胚理论,推导出二阶抛物线边值问题解存在唯一性的一个充分条件,从而推广了已经存在的一些定理.     

吸引盆在二阶抛物线边值问题解存在唯一性中的应用（英文）

本文研究了二阶抛物线边值问题解的存在唯一性的问题.利用吸引盆的方法和全局同胚理论,推导出二阶抛物线边值问题解存在唯一性的一个充分条件,从而推广了已经存在的一些定理.     

关于2n阶常微分方程两点边值问题解的存在性与唯一性

本文利用Leray－Schauder度理论建立了一类2n阶非线性常微分方程两点边值问题解的存在性与唯一性定理，以及利用Fredholm择一原理与Fourier展式，建立了一类2n阶线性常微分方程两点边值问题解的存在性唯一性定理．     

Schrdinger-Poisson问题的整体古典解

本文研究双Ｓｃｈｒｏｄｉｎｇｅｒ方程序列和Ｐｏｉｓｓｏｎ方程耦合的方程组的初边值问题, 利用不动点定理和嵌入定理,证明了其整体古典解的存在唯一性．     

Existence of solutions to second-order nonlinear discrete elliptic equations

In this paper, we consider a boundary value problem (BVP) for second-order nonlinear partial difference equations on finite lattice domains. Some conditions are established that ensure existence and uniqueness of solutions to the BVP under consideration.     

一类退化抛物方程的边值问题

In this paper, we study the boundary value problem (BVP) for a degenerate parabolic equation. By introducing a proper notion of weak solutions, we prove the uniqueness and existence of weak solutions of the problem. The localization of weak solutions is also discussed, which plays a key role in the proof of the uniqueness.     

角函数方法在二阶微分方程边值问题中的应用

利用角函数的方法讨论了下列二阶微分方程x″+g(t,x,x′)=0(1)x″+δsin(x)+h(t)=0(2)x″+g(t,x′)=0(3)在边界条件x(a)=x(b)=0(4)下解的存在性或唯一性问题.得到了边值问题(1)(4)的存在性定理,边值问题(2)(4)和(3)(4)的存在唯一性定理.     

边值问题的某些存在定理(英)

本文给出关于边值问题解的某存在唯一性定理及其应用．     

Existence and uniqueness of solutions to a nonlinear elliptic boundary value problem on time scales

In this paper, we consider a boundary value problem (BVP) for second-order nonlinear partial dynamic equations on the time scale rectangles. Some explicit conditions are established that ensure existence and uniqueness of solution to the BVP under consideration.     

u0 - 凹算子的不动点定理及其应用

该文利用锥的性质和单调迭代技巧讨论了u₀ - 凹算子正不动点的存在唯一性,所得结论改进并推广了已有的相关结果. 作为应用, 该文研究了一类Hammerstein积分方程正解的存在唯一性.     

Existence and uniqueness of solutions of differential equations with respect to non-additive measures

By taking Sugeno-derivative into account, first, we investigate the existence of solutions to the initial value problems (IVP) of first-order differential equations with respect to non-additive measure (more precisely, distorted Lebesgue measure). It particularly occurs in the mathematical modeling of biology. We begin by expressing the differential equation in terms of ordinary derivative and the derivative with respect to the distorted Lebesgue measure. Then, by using the fixed point theorem on cones, we construct an operator and prove the existence of positive non-decreasing solutions on cones in semi-order Banach spaces. In addition, we also use Picard–Lindelöf theorem to prove the existence and uniqueness of the solution of the equation. Second, we investigate the existence of a solution to the boundary value problem (BVP) on cones with integral boundary conditions of a mix-order differential equation with respect to non-additive measures. Moreover, the Krasnoselskii fixed point theorem is also applied to both BVP and IVP and obtains at least one positive non-decreasing solution. Examples with graphs are provided to validate the results.     

A Boundary Value Problem for Second Order Nonlinear Difference Equations on the Semi-infinite Interval

In this paper, we consider a boundary value problem (BVP) for nonlinear difference equations on the discrete semi-axis in which the left-hand side being a second order linear difference expression belongs to the so-called Weyl-Hamburger limit-circle case. The BVP is considered in the Hilbert space l 2 and is formed via boundary conditions at a starting point and at infinity. Existence and uniqueness results for solutions of the considered BVP are established.     

一类带积分边界条件的三阶微分方程边值问题的解

运用Banach压缩映射原理以及Leray-Schauder连续性原理,在非线性项为L1-Caratheodory函数的条件下,研究了一类带积分边界条件的三阶微分方程边值问题解的唯一性、存在性以及解集的紧性.     

EXISTENCE OF MILD SOLUTIONS TO NEUTRAL FRACTIONAL DIFFERENTIAL EQUATIONS WITH INFINITE DELAY

In this paper, we consider the existence of mild solution to a class of neutral fractional differential equations with infinite delay. By means of fixed points methods, we obtain some sufficient conditions for the existence and uniqueness of mild solutions, which extend some known results.