一类半线性分数Laplacian方程多解的存在性问题

本文研究了一类半线性分数Laplacian方程{(-△)~su=f(x,u),x∈Ω, u=0,x∈R~n\Ω在原点附近无穷多解的存在性问题.利用改进的Clark's定理,获得了方程对应的泛函有收敛于零的临界点序列的结果,推广了关于整数阶半线性方程多解的存在性结果.     

基于变分方法的奇异脉冲方程弱解的存在性

该文研究了一类具有扰动项的非线性奇异脉冲微分方程边值问题,利用变分方法结合临界点理论得到了弱解的存在性定理.     

非自治Caputo分数阶发展方程弱解的适定性与不变集

该文分析一族含有依赖时间参数t线性算子的时间分数阶非自治发展方程,利用Lions表示定理,得到了弱解适定性的充分条件;基于正交投影,建立了时间分数阶发展方程弱解的不变性准则.该文所研究方程中的算子是依赖时间的.     

Boussinesq方程解的部分正则性

本文考虑Boussinesq方程一类合适弱解的部分正则性.我们先运用广义能量不等式和奇异积分理论得到一些无维量的估计;再通过合适弱解满足的等式,运用迭代技巧,推导出温度场的小性估计;最后由尺度分析(scaling arguments)得到了一类合适弱解的部分正则性.     

一类分数阶Kirchhoff型方程非平凡解的存在性

利用临界点理论中的山路引理,研究一类分数阶Kirchhoff型方程在次临界增长条件下非平凡解的存在性,进一步统一和丰富了已有文献的相关结果.     

一类具有组合非线性项的分数阶方程的多重解（英文）

本文研究一类具有组合非线性项的分数阶Laplacian方程,在共振与非共振情形下,运用山路理论、Morse理论、Ekeland变分原理,建立了5个非平凡解的存在性结果.     

关于带权函数的的P—Laplacian方程的弱解的存在性问题

主要运用了山路引理,讨论了带特殊权函数的P—Laplacian方程的弱解的存在性问题．     

一类高阶非线性波动方程的时间周期问题

本文利用临界点理论证明一类高阶非线性波动方程时间周期弱解的存在性．     

一类Schodinger方程的唯一延拓性

本文研究一类具有Lip连续系数且带奇异位势的Schrodinger方程Lu=-div(A(x)△u)+V(x)u(x)=0,得到了此类方程弱解的唯一延拓性以及弱解的绝对值属于某Ap权.     

一类Schödinger方程的唯一延拓性

本文研究一类具有Lip连续系数且带奇异位势的Schrödinger方程Lu=-div(A(x)△u)+V(x)u(x)=0,得到了此类方程弱解的唯一延拓性以及弱解的绝对值属于某Ap权.     

Determining a Rotation of a Tetrahedron from a Projection

The following problem, arising from medical imaging, is addressed: Suppose that T is a known tetrahedron in ?³ with centroid at the origin. Also known is the orthogonal projection U of the vertices of the image ?T of T under an unknown rotation ? about the origin. Under what circumstances can ? be determined from T and U?     

On a mapping of a projective space into a sphere

We obtain an exact estimate for the minimum multiplicity of a continuous finite-to-one mapping of a projective space into a sphere for all dimensions. For finite-to-one mappings of a projective space into a Euclidean space, we obtain an exact estimate for this multiplicity for n = 2, 3. For n ≥ 4, we prove that this estimate does not exceed 4. Several open questions are formulated.     

Calculating a function of a matrix with a real spectrum

Let T be a square matrix with a real spectrum, and let f be an analytic function. The problem of the approximate calculation of f(T) is discussed. Applying the Schur triangular decomposition and the reordering, one can assume that T is triangular and its diagonal entries t_ii are arranged in increasing order. To avoid calculations using the differences t_ii ? t_jj with close (including equal) t_ii and t_jj, it is proposed to represent T in a block form and calculate the two main block diagonals using interpolating polynomials. The rest of the f(T) entries can be calculated using the Parlett recurrence algorithm. It is also proposed to perform some scalar operations (such as the building of interpolating polynomials) with an enlarged number of significant decimal digits.

     

Evolution to a steady state for a rarefied gas flowing from a tank into a vacuum through a plane channel

A kinetic equation (S-model) is used to solve the nonstationary problem of a monatomic rarefied gas flowing from a tank of infinite capacity into a vacuum through a long plane channel. Initially, the gas is at rest and is separated from the vacuum by a barrier. The temperature of the channel walls is kept constant. The flow is found to evolve to a steady state. The time required for reaching a steady state is examined depending on the channel length and the degree of gas rarefaction. The kinetic equation is solved numerically by applying a conservative explicit finite-difference scheme that is firstorder accurate in time and second-order accurate in space. An approximate law is proposed for the asymptotic behavior of the solution at long times when the evolution to a steady state becomes a diffusion process.