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 .     

一个椭圆特征问题解对参数的连续性

用变分方法证明了一个限制在球面上的椭圆特征问题解对参数（球面半径）的连续性，从而得到相应的不带限制的椭圆特征问题的解分枝。     

Existence and Regularity of Solutions of a Nonlinear Nonuniformly Elliptic System Arising from a Thermistor Problem

A thermistor is an electric circuit device made of ceramic material whose electric conductivity depends on the temperature. If the only heat source is the electric heating, the temperature and the electric potential satisfy a nonlinear elliptic system which is also degenerate if the electric conductivity is not uniformly bounded from above or away from zero. Under general boundary conditions, we establish existence and Hölder continuity of solutions of such a nonlinear nonuniformly elliptic system. When the elechic conductivity linearly depends on the temperature, we provide a non-uniqueness and non-existence example.     

On the Dirichlet Problem for a System of Degenerate at a Point Elliptic Equations in the Class of Bounded Functions

We consider a weakly connected (by the lowest terms) system of elliptic equations of second order with the main part in the form of the Laplace operator, the order of which becomes degenerate at an interior point of the domain. We investigate a Dirichlet-type problem in the class of bounded Hölder vector functions. We obtain sufficient conditions for the existence and uniqueness of a solution.     

Preconditioning Mixed Finite Element Saddle-point Elliptic Problems

We consider saddle-point problems that typically arise from the mixed finite element discretization of second-order elliptic problems. By proper equivalent algebraic operations the considered saddle-point problem is transformed to another saddle-point problem. The resulting problem can then be efficiently preconditioned by a block-diagonal matrix or by a factored block-matrix (the blocks correspond to the velocity and pressure, respectively). Both preconditioners have a block on the main diagonal that corresponds to the bilinear form (δ is a positive parameter) and a second block that is equal to a constant times the identity operator. We derive uniform bounds for the negative and positive eigenvalues of the preconditioned operator. Then any known preconditioner for the above bilinear form can be applied. We also show some numerical experiments that illustrate the convergence properties of the proposed technique.     

退化的非线性椭圆方程的径向解

利用打靶法讨论一类退化非线性椭圆型方程径向解的性态，得出了径向解的间断及不间断的结果．     

拟线性椭圆型方程带有混合奇异项的正整体解

在本文中,研究了方程div(｜u｜p-2u) f(x,u)=0,x∈RN,N≥3的正整体解,其中f(x,u)在u=0未假定是正则的,且f(x,u)可以同时包含超线性,亚线性项和奇异项.     

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。     

Superlinear Fourth-Order Elliptic Problem Without Ambrosetti and Rabinowitz Growth Condition

This paper deals with superlinear fourth-order elliptic problem under Navier boundary condition. By using the mountain pass theorem and suitable truncation, a multiplicity result is established for all $λ > 0$ and some previous result is extended.     

半线性椭圆方程的正解

本文用特征理论及上下解方法,证明了一类半线性椭圆方程边值问题的正解的存在性,同时给出了解的估计.     

二阶复椭圆Riemann—Hilbert边值问题

讨论了一般二阶非线性椭圆复方程的Riemann-Hilbert边值问题,首先给出Riemann-Hilbert问题及其适应性的概念,其次给出改进后的边值问题解的表述并证明了它的可解性,最后导出原Rremann-Hilbert边值问题的可解条件。     

Existence of Entire Solutions of a Singular Semilinear Elliptic Problem

In this paper, we obtain some existence results for a class of singular semilinear elliptic problems where we improve some earlier results of Zhijun Zhang. We show the existence of entire positive solutions without the monotonic condition imposed in Zhang‘s paper. The main point of our technique is to choose an approximating sequence and prove its convergence. The desired compactness can be obtained by the Sobolev embedding theorems.     

一类四阶非线性椭圆问题变号解的存在性

通过建立一个新空间,在新空间中讨论了一个含Hardy位势的四阶非线性椭圆问题变号解的存在性.在一个环绕定理下,得到了问题变号解的存在性.     

带Hardy项的半线性椭圆方程非球对称解的研究

本文考虑如下带Hardy项的半线性椭圆问题{-Δu-μu/|x|2=f(u), x∈Ω,/ u=0,x∈(6)Ω}非球对称解的存在性.这里Ω={x|x∈Rn,n≥3,a＜|x|＜1}是Rn≥3)中的环,其中0≤μ＜μ=(n-2/2)2,f(u)为已知函数.本文在讨论球对称解的性质的基础上,利用变分方法得到了方程的极小能量解的存在性,并且利用分支理论得到了方程的非球对称解.     

Large and Small Solutions of a Class of Quasilinear Elliptic Eigenvalue Problems

Existence and uniqueness results for large positive solutions are obtained for a class of quasilinear elliptic eigenvalue problems in general bounded smooth domains via a generalization of a sweeping principle of Serrin. The nonlinear terms of the problems can be negative in some intervals. The existence and structure of a mountain pass solution are also discussed. We show that this solution develops to a spike layer solution.     

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

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Existence of Viscosity Solutions of Second Order Fully Nonlinear Elliptic Equations

We consider the problem of existence for viscosity solutions of seoond order fully nonlinear elliptic partial differential equations F(D²u, Du, u, z) = 0. We prove existence results for viscosity solutions in W^{1,∞} under assumptions that function F satisfies the natural structure conditions. We do not assume F is convex.     

退化椭圆问题的最小二乘混合有限元方法

本文研究了电磁场中关于共振现象的一类退化的椭圆问题 ,提出了最小二乘混合有限元方法 .这一方法的好处是可以去掉传统混合元空间的LBB条件所得到的系数矩阵是对称正定的 ,使得法语解更加方便 .本文得到了最小二乘混合有限元方法的L2 和H1估计 .     

由p-Laplacian算子导出的半变分不等式的特征值问题

研究了一类具有非光滑局部Lipschitz位势(半变分不等式)的非线性特征值问题其中1相似文献