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     

Positive Solutions of Fully Nonlinear Elliptic Equations on General Bounded Domains

We prove the refined ABP maximum principle, comparison principle, and related existence and uniqueness theorem for the positive solutions of the Dirichlet problems of second order fully nonlinear elliptic equations on arbitrary bounded domains.     

球外部区域上非线性椭圆型方程的正径向解

本文讨论球外部区域Ω={x∈RN||x|>R}上非线性椭圆边值问题正径向解的存在性,其中g(r),f(u)为非负连续函数.在g(r)满足条件0<∫R∞rg(r)dr<∞,f(u)关于u超线性或次线性增长的情形,获得了该问题正径向解的存在性.     

关于半线性椭圆型方程爆破解的存在性

文中得到半线性椭圆型方程的爆破问题解的存在性,其中或者是Rn中的有界区域,C3,C4,C5,C6是正常数,并且C5,C3（0,1）．     

一类半线性椭圆方程正解的唯一性

本文应用延拓方法证明了一类半线性椭圆方程正解的唯一性,改进了已有结果．     

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。     

Positive Solutions of Nonlinear Elliptic Equations in Unbounded Domains in R 2

We study the existence of positive solutions of the nonlinear equation u+f(,u)=0, in D with u=0 on D, where D is an unbounded domain in R ² with a compact nonempty boundary D consisting of finitely many Jordan curves. The aim is to prove an existence result for the above equation in a general setting by using potential theory.     

一种奇异临界椭圆方程的非平凡解

该文研究了一类带有Sobolev-Hardy临界指数的半线性椭圆方程,运用变分理论中的环绕定理证明了方程非平凡解的存在性     

临界增长条件下一类半线性椭圆方程解的存在性

用变分方法研究了半线性椭圆方程Dirichlet迫值同题-△μ=f(x,μ） h（x）对几乎所有的x∈Ω，μ=0在δΩ上解的存在性，在临界增长情况下得到了所解的一个存在性定理．     

一类半线性椭圆方程的正径向解

本文以关于非线性全连续算子的锥不动点定理为工具，研究半线性椭圆边值问题上Δu λa(|x|)u f(|x|,u)=0(x∈Ω)，u|=0及Δu λf(|x|,u)=0(x∈Ω)，u|=0．在不假定f单调的情况下，本文得出了上述问题存在正径向解的若干充分条件．     

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.     

在环域内一类拟线性椭圆型方程正对称解的存在性

利用Ｌｅｒａｙ－Ｓｃｈａｕｄｅｒ不动点定理和变分法得到了边值问题正对称解的存在性,这里　是ＩＲ~Ｎ中的环城．     

全空间上一类半线性椭圆方程的正解

本文研究Rn(n≥ 3)上的半线性椭圆方程 -Δu=f(u)的C2 正解 .如果f(u)在 ( 0 ,∞ )上局部有界并且对某个α 1 <α相似文献   

一类非线性二阶椭圆型方程组的正解

本文讨论二阶非线性椭圆边值问题的正解的存在性,其中非线性项f和g关于u,v的增长限制很不相同.f是超线性的,而g满足次线性的条件.利用拓扑度理论和上、下解方法,得到了几个正解的存在性定理.作为应用,本文还给出了一些具体的例子.     

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.     

On the Interior Smoothness of Solutions to Second-Order Elliptic Equations

We study the interior smoothness properties of solutions to a linear second-order uniformly elliptic equation in selfadjoint form without lower-order terms and with measurable bounded coefficients. In terms of membership in a special function space we combine and supplement some properties of solutions such as membership in the Sobolev space W _{2, loc} ¹ and Holder continuity. We show that the membership of solutions in the introduced space which we establish in this article gives some new properties that do not follow from Holder continuity and the membership in W _2,loc ¹ .     

Limits at Infinity of Superharmonic Functions and Solutions of Semilinear Elliptic Equations of Matukuma Type

In an unbounded domain Ω in ℝ ⁿ (n ≥ 2) with a compact boundary or Ω = ℝ ⁿ , we investigate the existence of limits at infinity of positive superharmonic functions u on Ω satisfying a nonlinear inequality like as

具临界Sobolev-Hardy指数的半线性椭圆方程的非平凡解

本文研究了如下问题：-div（｜x｜β△u）=｜x｜^a｜u｜^2（α,β）-2u＋λ｜x｜σ｜u｜^q-2,x∈Ω,u=0,x∈δΩ,这里Ω∪→R^N是有界光滑区域且0∈Ω，2（α，β）=2（N＋α）/N＋β-2，运用Sobolev-Hardy不等式和山路几何，证明了在一定的条件下方程至少存在一个非平凡解。     

On Localization of Solutions of Elliptic Equations with Nonhomogeneous Anisotropic Degeneracy

The work deals with the Dirichlet problem for elliptic equations with nonhomogeneous anisotropic degeneracy in a possibly unbounded domain of multidimensional Euclidean space. The existence of weak solutions is proved. Some conditions are established connecting the character of nonlinearity of the equation and the geometric characteristics of the domain which guarantee the one-dimensional localization (vanishing) of weak solutions. The equation with anisotropic degeneracy is shown to admit localized solutions even in the absence of absorption.