在无界区域上拟线性散度型椭圆型方程的Dirichlet问题

研究在无界区域上的二阶拟线性散度型椭圆型方程Dirichlet问题在无穷远处径向收敛的古典解存在性和唯一性。     

Dirichlet Problem for a Class of Quasilinear Elliptic Equations

In this paper, the Dirichlet problem for quasilinear elliptic equations is studied. New a priori estimates of the solution and its gradient are obtained. These estimates are derived without any assumptions on the smoothness of the coefficients and the right-hand side of the equation. Moreover, an arbitrary growth of the right-hand side with respect to the gradient of the solution is assumed. On the basis of the resulting estimates, existence theorems are proved.     

Dirichlet Problem for Degenerate Quasilinear Elliptic Equations Suggested by the Anisotropic Permeation

By Browder's pseudo-monotone operator theory and the techniques belonging to J. Leray and J. Lions, the existence theorem of the generalized solution of the Dirichlet problem for a strongly degenerate quasilincar elliptic equation has been proved in the anisotropic Sobolev space.     

一类拟线性椭圆方程组的Dirichlet问题

The homogeneous Dirichlet problem(1) for quasilinear elliptic system in a bounded domain Ω is investigated in this paper. The existence of generalized solutions in [H₀¹(Ω)]^N is obtained by using the contructive Galerkin method. For the case of a_ij^lm=0 when i≠j, it is estatablished that such generalized solutions have bounded [L_∞(Ω)]N norm and possess Holeler continuity. Even in the particular case that f_i are independent of Du, our results have improved those of A. V. Lair [Ann. Mat. Pura Appl., 116(1978)], allowing b_i¹(x,u) and f_i(x,u) to have a growth in u arbitrarily close to 1.     

双退化拟线性椭圆型方程Keldys-Fichera障碍问题

讨论一类双退化散度型拟线性椭圆型方程的Keldys-Fichera障碍问题,证明了解的存在性.     

双退化拟线性椭圆型方程Keldys-Fichera障碍问题

讨论一类双退化散度型拟线性椭圆型方程的Keldys-Fichera障碍问题,证明了解的存在性.     

Two Positive Solutions of a Quasilinear Elliptic Dirichlet Problem

For a class of second order quasilinear elliptic equations we establish the existence of two non–negative weak solutions of the Dirichlet problem on a bounded domain, Ω. Solutions of the boundary value problem are critical points of C ¹–functional on H₀¹(W){H_0^1(Omega)}. One solution is a local minimum and the other is of mountain pass type.     

在环形区域上的半线性椭圆型方程边值问题

该文讨论半线性椭圆型方程在环形区域上的Dirichlet(dirchlet-Neumann)边值问题．     

关于含小参数的拟线性椭圆型方程的狄立克雷问题

本文研究最高阶导数项含小参数的拟线性椭圆型方程的狄立克雷问题,在退化方程的特征是曲线和区域是凸域的一般情形下,给出构造一致有效渐近解的方法,并证明当小参数是充分小时,狄立克雷问题的解是存在和唯一.     

环域上一类拟线性椭圆方程正的径向解的多重性

研究了方程-div(‖Du‖^-2Du)=λf(u)在R^n,n≥2中环域上的正的径向解的多重性。当f在正区域上有多个峰的情况下,我们获得了多个解。     

Neumann Problem of Quasilinear Elliptic Equations with Limit Nonlinearity in Boundary Condition

This paper is concerned with the existence of solutions to the equation D_j(a^{ij}(x,u)D_i,u)-\frac{1}{2}D_sa^{ij}(x,u)D_iuD_ju + λ u = 0 on a bounded domain under the Neumann boundary condition a{ij}(x,u)D_iuϒ_j = lul^{\frac{2}{n-2}}u.     

The Conormal Derivative Problem for Elliptic Equations with BMO Coefficients on Reifenberg Flat Domains

We study the inhomogeneous conormal derivative problem for thedivergence form elliptic equation, assuming that the principalcoefficients belong to the BMO space with small BMO semi-normsand that the boundary is -Reifenberg flat. These conditionsfor the W^{1, p}-theory not only weaken the requirements on thecoefficients but also lead to a more general geometric conditionon the domain. In fact, the Reifenberg flatness is the minimalregularity condition for the W^{1, p}-theory. 2000 MathematicsSubject Classification 35R05 (primary), 35J15 (secondary).     

On the Robin Problem for Second-Order Elliptic Equations in Cylindrical Domains

In a semi-infinite cylinder, we consider the behavior of generalized solutions of second-order divergence-form elliptic equations satisfying the third boundary condition on the lateral surface of the cylinder.     

Behavior of Solutions to the Dirichlet Problem for Elliptic Systems in Convex Domains

We consider the Dirichlet problem for strongly elliptic systems of order 2m in convex domains. Under a positivity assumption on the Poisson kernel it is proved that the weak solution has bounded derivatives up to order m provided the outward unit normal has no big jumps on the boundary. In the case of second order symmetric systems in plane convex domains the boundedness of the first derivatives is proved without the assumption on the normal.     

Uniqueness and Flat Core of Positive Solutions for Quasilinear Elliptic Eigenvalue Problems in General Smooth Domains

The structure of positive solutions to the quasilinear elliptic problems –div(|Du|^p–2Du = λf(u) in Ω, u = 0 on ∂Ω, p > 1, Ω ⊂ R^Na bounded smooth domain, is precisely studied when λ is sufficiently large, for a class of logistic‐type nonlinearities f(u) satisfying that f(0) = f(a) = 0, a > 0, f(u) > 0 for u ∈ (0,a), , while u = a is a zero point of f with order ω. It is shown that if ω ≥ p – 1, the problem has a unique positive solution u_λ with sup _Ω u_λ < a, which develops a boundary layer near ∂Ω. It is shown that if 0 < ω < p – 1, the problem also has a unique positive solution u _λ, but the flat core {x ∈ Ω : u_λ(x) = a} ≠ ∅︁ exists. Moreover, the asymptotic behaviour of the flat core is studied as λ → ∞.