Non-existence Results for Quasilinear Elliptic Equations in Unbounded Domains

In the middle of 1980s,Ni＆Serrin,Grads,Ni ＆Nirenberg,established a generalized iueqnality for the sphelrical symmetry Solutions of quasilinear elliptic equations diV[A(|Du|)] ,f(u)=0,χ∈~n (1) By using this inequality,the results that do not exist spherical symmetry solution can be Proved.In order to study the non-existence of the nonspherical symmetry Solutions,We must establish the Pohozaev' ideutity or inequality for general nonspherical symmetry SOlutions for the most general quasilinear Euler equations     

一类含权Rellich不等式

本文证明了一类含权Rellich不等式,其中的常数是最佳的.     

调和映射中的弱单调不等式和部分正则性

对弱调和映射引入局部弱单调不等式的概念 ,并得到了这类弱调和映射的一些结果 ,如局部弱单调不等式几乎等价于ε-正则性等 .     

R~4中含位势的非线性双调和方程

建立了H02(Ω)(0∈ΩR4)中的Hardy不等式,利用临界点理论得到了含位势的非线性双调和方程非平凡解的存在性.     

退化变分问题和退化椭圆型方程的正解

本文讨论由未知函数u=0引起的下列退化变分问题正解的存在性: 证明此正解满足Harnack不等式性质,进一步讨论带自然增长退化椭圆型Euler方程具下列非齐次Dirichlet问题解的存在性:     

p阶平均曲率算子Dirichlet问题的无穷多个解

§ 1　 IntroductionSince the Mountain Pass Theorem came out,the existence of nontrivial solutions,pos-sibly multiple,ofnonlinear elliptic equations has been extensively studied.In this paper,weconsider the following Dirichlet problem for p-(generalized) mean curvature operator:-div((1 +| u|2 ) p- 22 u) =f(x,u) ,　 x∈Ω,u∈ W1 ,p0 (Ω ) , (1 .1 )whereΩ is a bounded domain in Rn(n>p>1 ) with smooth boundary Ω.First let us recall the following Dirichletproblem for p-Laplacian:-Δpu≡ -div…     

泛函∫_ΩF(x,u,Du)dx的非平凡临界点的讨论

本文研究了泛函非平凡临界点的存在性.本文的结论的条件要比文献[1]—[4]的弱,如对泛函,条件u·g(x,u)-pG(x,u)≥-c可以取代条件u·g(x,u)-μG(x,u)≥-c,μ>p。     

WEIGHTED POINCARE INEQUALITIES, ON UNBOUNDED DOMAINS AND NONLINEAR ELLIPTIC BOUNDARY VALUE, PROBLEMS

This paper is concerned with establishing Poincare type inequalities for integrals of functions and their derivatives over unbounded domains.It is well know that the Poincare inequality     

R2中含临界位势的非线性椭圆问题

考虑R²中的含临界位势的非线性椭圆方程齐次Dirichlet问题. 通过建立一常数为最佳的含权不等式, 确定了临界位势, 并讨论了含临界位势的Laplace方程特征值问题. 通过建立含一个奇点的解的Pohozaev型恒等式并结合Cauchy-Kovalevskaya定理得到了含临界位势非线性椭圆型方程有奇点的解的不存在性结果. 此外, 利用山路定理和特征值的性质得到了这一问题多重解的存在性的一系列结果.     

拟线性椭圆型方程组奇性解的Pohozaev恒等式与解不存在性

该文分别研究了超临界指数和自然增长条件下拟线椭圆型方程组奇性解成立Poho-zaev恒等式的一些充分条件．