Heisenberg群上拟线性次椭圆方程的可解性

该文通过山路引理给出了加权次椭圆Ｓｏｂｏｌｅｖ空间上拟线性方程解的存在性结果     

Heisenberg群上具VMO系数的退化椭圆方程的Morrey正则性

本文研究Heisenberg群上具有VMO(零平均振荡)系数的非散度型退化椭圆方程.通过证明适当的Sobolev-Poincaré型不等式,建立方程的Lp正则性;然后利用初等方法,得到退化椭圆方程解的Morrey正则性.     

Heisenberg群上次椭圆p-Laplace方程的边界估计

研究次椭圆p-Laplace方程(P＞1)解的边界性质,通过建立Heisenberg群上带有区域内点到边界Carnot-Carath閛dory距离函数的Hardy型不等式,给出了有界域上次椭圆p-Laplace方程以及带非平凡位势的次椭圆p-Laplace方程的解在边界附近的若干估计.     

一类椭圆退缩方程的可解性

本文建立了高阶项与低阶项同时退缩的Sobolev嵌入定理，给出了精圈退缩方程可解性的充分条件，并利用Leray-Lions方法得到了解的存在性．     

Heisenberg群上一类含有临界Sobolev指数拟线性椭圆方程存在性定理

研究了Heisenberg群上一类含有临界Sobolev指数的偏微分方程解的存在性问题.利用Nehari流形以及极值原理,证明了在不同的条件下,方程至少存在一个或两个正解.     

一类零点为次线性的椭圆方程的可解性

该文考虑-Δu =g(x) |u|q- 2 u λ|u|p- 2 u f(x) ,x∈Ω,u| Ω =0 ,g,f∈ L∞ (Ω ) ,1 相似文献   

Heisenberg群上四阶非线性方程特征值问题的正解

本文通过Leray-Schauder度,给出Heisenberg群上四阶非线性次椭圆方程特征值问题的正解的一些存在性结果.     

Heisenberg群上四阶非线性方程特征值问题的正解

本文通过Ｌｅｒａｙ－Ｓｃｈａｕｄｅｒ度,给出Ｈｅｉｓｅｎｂｅｒｇ群上四阶非线性次椭圆方程特征值问题的正解的一些存在性结果．     

Existence Results for the Positive Solutions of a Fourth Order Nonlinear Equations on the Heisenberg Group

In this paper, we give some existence results for a fourth order nonlinear subelliptic equations on the Heisenberg group by the Leray-Schauder degree.     

Solvability on the Heisenberg group

We solve in various spaces the linear equations L_αg = f , where L_α belongs to a class of transversally elliptic second order differential operators on the Heisenberg group with double characteristics and complex‐valued coefficients, not necessarily locally solvable. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Nonexistence results for higher order pseudo‐parabolic equations in the Heisenberg group

Sufficient conditions are obtained for the nonexistence of solutions to the nonlinear higher order pseudo‐parabolic equation where is the Kohn‐Laplace operator on the (2N + 1)‐dimensional Heisenberg group , m≥1,p > 1. Then, this result is extended to the case of a 2 × 2‐system of the same type. Our technique of proof is based on judicious choices of the test functions in the weak formulation of the sought solutions. Copyright © 2016 John Wiley & Sons, Ltd.     

On the global existence of solution to one-dimensional fourth order nonlinear Sobolev type equations

We prove the global existence and uniqueness of a classical solution to initial boundary value problem for a class of Sobolev type equations under the Dirichlet boundary conditions. This class of evolution equations covers the well-known viscous Cahn-Hilliard equation and the viscous Camassa-Holm equation.     

Oscillation of fourth order nonlinear neutral difference equations I

Oscillatory and asymptotic behaviour of solutions of a class of nonlinear fourth order neutral difference equations of the form

一类带位势非线性热方程解的不存在性定理

研究与向量场有关的非线性次椭圆热方程.通过选取合适的测试函数,应用反证法证明了与之相关的初边值问题解的不存在性定理,将欧式空间及Heisenberg群上的结果推广至满足H（o）rmander有限秩条件的光滑向量场.     

Hardy type and Rellich type inequalities on the Heisenberg group

This paper contains some interesting Hardy type inequalities and Rellich type inequalities for the left invariant vector fields on the Heisenberg group.

     

EXISTENCE OF SOLUTIONS OF NONLINEAR TWO AND THREE-POINT BOUNDARY VALUE PROBLEMS FOR FOURTH ORDER NONLINEAR DIFFERENTIAL EQUATIONS

In this paper, the two and three-point boundsry problems (with nonlinear boundary conditions)for the genaral noniinear equations of fourth order are discussed.We have set some grups of the assurnpion coditions and proved the existence of solutins for corresponding boundary value problems under these conditons.     

Wellposedness for the fourth order nonlinear Schrödinger equations

We study the local smoothing effects and wellposedness of Cauchy problem for the fourth order nonlinear Schrödinger equations in 1D