自共轭椭圆型方程的样条解法

本文从二元样条空间的理论出发,构造了一类新的差分格式,并利用它得到了一类自共轭椭圆型方程的样条解,并证明了这样的解的唯一性和收敛性问题.最后,给出了一个数值例子,说明了本方法是可行的.     

On the Existence of Positive Solutions for a Class of Semilinear Elliptic Systems

We study the existence of positive solutions for a class of semilinear ellipcic systems in general domains via the blow up argument and degree theory. The main idea can be used to establish the existence of positive solutions for the Navier problems of polyharmonic semilinear equations in general domains.     

二阶椭圆方程的振动准则

本文考虑带有强迫项的半线性椭圆型方程△u c(x,u)=f(x)解的振动性质。证明了在适当条下,存在一个环形区域的无穷序列,使得方程的每一个解在每一个环形区域内均有一个零点。     

非线性发展方程的Jacobi椭圆函数解

借助齐次平衡原则,提出了一种新的构造非线性发展方程的Jacobi椭圆函数精确解的方法.并利用之得到了KdV方程,Boussinesq方程,KGS方程组的新形式Jacobi椭圆函数解.     

二阶含阻尼项椭圆型方程的区域振动准则

籍用平均函数和积分算子, 对二阶含阻尼项椭圆型微分方程∑^N_{i,j=1}{D_i[a_{ij}(x)D_j{y}]+∑^N_{i=1}b_i (x)D_i{y}+q(x)f(y)=0建立了一些区域振动准则, 这些准则不同于已知的依赖于整个区域Ω(1)的性质的结果,而是仅依赖于区域Ω(1)的一列子区域的性质.     

A Lyapunov Lemma for Elliptic Systems

We study a possible extension to the infinite-dimensional case of the classicalLyapunov lemma for matrices. More precisely, for a fixed elliptic system A ofdifferential operators of order m, we consider the operator equationTA + A ^* T = Q, where Q is any given classical pseudodifferential system oforder m, and T is sought as a classical pseudodifferential system of order0.     

The Riemann Hilbert Problem for General Elliptic Complex Equations of Fourth Order

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Multiple Solutions for a Class of Semilinear Elliptic Equations

We show that for a class of semilinear elliptic equations there are at least three nontrivial solutions. Existence of infinitely many solutions is also shown when the nonlinear term is odd. In our results, the nonlinear term can grow super-critically at infinity.

     

一类非线性椭圆方程解的存在性

本文考虑一类非线性椭圆方程,运用强制变分方法,我们给出了在多种情况下方程解的存在性。     

On the Rate of Convergence of Finite-Difference Approximations for Elliptic Isaacs Equations in Smooth Domains

We show that there exists an algebraic rate of convergence of solutions of finite-difference approximations for uniformly elliptic Isaacs equations in smooth bounded domains.     

On Blow Up Solutions of a Quasilinear Elliptic Equation

Given a bounded regular domain Ω in ℝ^N, we study existence and asymptotic behaviour of the solutions of the equation Δu + |Du|^q = f(u) in Ω, which diverge on ∂Ω. We extend and complete some results contained in [4].     

A Comparison Theorem for an Elliptic Operator

In this note, using ₂ (Bakry–Emery curvature operator) and the classical maximum principle, we establish a comparison estimate for a general elliptic operator on a manifold, without using Jacobi field theory.     

临界情形的非齐次半线性椭圆型方程的多解性

考虑有界区域Ω RN 上非齐次半线性椭圆型方程 -Δu(x) =up(x) λf(x)在齐次混合边值条件 (即第三边值问题 ) u n au Ω =0下正解的存在性 ,其中α ,λ≥ 0 ,p=N 2N- 2 ,N>2 ,f(x) ∈L∞(Ω) .证明了存在常数λ >0 ,当λ∈ (0 ,λ )时 ,上述问题至少存在两个正解     

二阶拟线性椭圆型方程振动性的积分平均方法

§ 1.　IntroductionThepurposeofthispaperistostudytheoscillatorybehaviorofsolutionsofcertainquasi linearellipticequationsdiv( ｜Du｜m -2 A(x)Du) + p(x) ｜u｜m -2 u=0 ,x∈Ω Rn,(E)whereΩisanexteriordomain ,m >1 ,andfunctionsA(x) ,p(x)aretobespecifiedinthefollowingtext.Recently ,USAMI [6]consideredEq .(E)whenA(x)≡I (identitymatrix) ,andob tainedoscillationcriteriaforEq .(E)with“infiniteintegral”coefficient [cf.[6],Theorem 4].However,asfarasthepresentreferencesisconcerned ,therearefewo…     

Strong Solution of the Obstacle Problem for Fully Nonlinear Elliptic Equations

In this paper we obtain the existence of W^{2, ∞} solutions of the obstacle problems for fully nonlinear elliptic equations under more general structure conditions than those in [1] by using the mollifier approach, which is also extended in our discussion.     

一类奇异临界椭圆方程非平凡解的存在性

研究了一类带Sobolev-Hardy临界指数的奇异椭圆方程,应用变分方法,通过能量估计和证明对应的能量泛函满足(PS)_c条件,运用山路引理得到了这类方程非平凡解的存在性.     

一类非线性四阶椭圆型方程的极值原理及其特征值问题

主要应用 Hopf极值原理 ,对一类非线性四阶椭圆型方程Δ2 u +h( x,u,Δu) =0进行研究 ,得到解的泛函的极值原理 .类似的文章结果也有许多 ,其方法均为构造适当的“P-泛函”,但是以前的结果都对方程有较强的要求限制 .本文通过构造新的泛函 ,减弱了要求限制 .同时对方程Δ2 u +λh( x,u,Δu) =0的特征值给出了估计 .