Non-coercive Linear Elliptic Problems

We study here some linear elliptic partial differential equations (with Dirichlet, Fourier or mixed boundary conditions), to which convection terms (first order perturbations) are added that entail the loss of the classical coercivity property. We prove the existence, uniqueness and regularity results for the solutions to these problems.     

系数变号的半线性椭圆方程的正解

本文研究半线性椭圆方程Dirichlet问题-△u=α（x）f(u），x∈Ω， u（x）=0，x∈ЭΩ，正解的存在性，其中Ω为R^n中有界的带光滑边界的区域，α(x)可以变号。     

ON THE HYPERBOLIC OBSTACLE PROBLEM OF FIRST ORDER

InroductlonThe classical obstacle problem canbe formulated as the     

ON THE UNIQUENESS OF THE WEAK SOLUTIONS OF A QUASILINEAR HYPERBOLIC SYSTEM WITH A SINGULAR SOURCE TERM

This paper is a continuation of the authors'previous paper[1].In this paper the authorsprove,assuming additional conditions on the initial data,some results about the existence anduniqueness of the entropy weak solutions of the Cauchy problem for the singular hyperbolicsystem a_t+(au)_x_2au/x=0,u_t+1/2(a~2+u~2)_x=0,x>0,t≥0.     

Almost automorphic solutions of evolution equations

This paper is concerned with the existence of almost automorphic mild solutions to equations of the form

where generates a holomorphic semigroup and is an almost automorphic function. Since almost automorphic functions may not be uniformly continuous, we introduce the notion of the uniform spectrum of a function. By modifying the method of sums of commuting operators used in previous works for the case of bounded uniformly continuous solutions, we obtain sufficient conditions for the existence of almost automorphic mild solutions to in terms of the imaginary spectrum of and the uniform spectrum of .

     

与A-调和方程有关的两个结果

给出两个与A 调和方程有关的结果 .第一个结果是一类A 调和方程的很弱解可由调和函数逼近 .另一个是变分积分弱极值的充分必要条件     

Exact multiplicity for periodic solutions of a first-order differential equation

Consider the differential equation

(1)     

一类奇摄动方程的PLK方法

通过对坐标作包含因变量的非线性泛函的变换,以首项渐近解和相应的坐标变换给出原问题的二阶的近似解,并把这种思想进一步推广到更复杂的非线性方程,用较为简洁的方法求得了一类非线性方程的二阶渐近解.     

一类两点边值问题的多重非负解

该文考虑两点边值问题[1/q(t)][q(t)y′(t)]′+p(t)f(y(t))= 0,λ_1 y(α)-λ_2y′(α)=0 and y(β)=B非负解的存在性, 其中p(t)可能在t=α或t=β附近具有奇异性, f(0)≥0, lim_(y→+∞)f(y)/y=+∞, 并且存在y>0, 使得f(y)<0.      

复Ginzburg Landau方程的自相似解及其极限行为

该文证明了复Ginzburg Landau方程在非标准的函数空间X_{s,p}中整体解的存在唯一性；考察了其解在X_{0,α+2}中的极限行为，得到当参数ε→0++或a→0, ε→0++时，Ginzburg Landau方程的解关于时间一致收敛到相应极限方程的解