Pohozaev恒等式及其在非线性椭圆型方程中的应用

在非线性椭圆型偏微分方程的研究中,Pohozaev恒等式在研究非平凡解的存在性和非存在性时起着十分重要的作用.本文旨在介绍Pohozaev恒等式及其在非线性椭圆型问题研究中的应用.首先介绍有界区域和无界区域上几种典型的Pohozaev恒等式,并得到几类非线性椭圆型方程存在解的必要条件,进而得到对应的方程非平凡解的非存在性和存在性结果.其次将介绍非线性椭圆型方程的局部Pohozaev恒等式,由此证明非线性椭圆型微分方程近似解序列的紧性,并得到几类典型非线性椭圆型方程的无穷多解存在性.最后利用非线性椭圆型方程的局部Pohozaev恒等式来研究其波峰解,得到波峰解的局部唯一性,并由此判断波峰解的对称性等特征.     

非线性椭圆型方程组边值问题的可解性

研究椭圆型方程组Dirichlet边值问题的可解性,利用不动点定理证明了上述问题存在上、下解情形,存在有界非负解,并利用该结论讨论了带参数的椭圆型方程组Dirichlet边值问题通过寻找该问题的上、下解,证明了正参数充分小时,这个问题存在有界正解.这里非线性函数在+∞处可以是超线性的,从而证明了部分椭圆型方程组边值问题中非线性项为超线性时,有界正解的存在性.同时,作为定理的应用,给出了实例.     

具有两个临界指数问题正径向解的存在性

本文中,我们提出了一个具有两种临界指数的非线性椭圆型方程问题,证明了狄氏问题的正径向解的存在性。     

二阶椭圆型方程组的第三边值问题

本文中,我们讨论二阶非线性一致椭圆型方程组(1.1)在多连通区域上的第三边值问题(问题Ⅲ)。首先,我们证明了调和函数问题Ⅲ解的存在唯一性,并建立了方程组(1.1)问题Ⅲ解的积分表示。然后,使用上述结果,方程组(1.1)问题Ⅲ解的先验估计以及Leray-Schauder定理,我们得到了满足某些条件的二阶非线性椭圆型方程组(1.1)问题Ⅲ的可解性结果。     

关于高维非线性椭圆型方程的正整解

建立一类高维二阶非线性椭圆型方程正整解的存在性定理，并给出解的有关性质．     

拟线性椭圆型议程组正整体解的存在性

本文讨论了一类满足初值条件的非线性椭圆型方程组正整体解的存在性.     

具有非线性梯度项的半线性椭圆型方程的爆炸解

本文在经典摄动方法与椭圆型偏微分方程的估计理论的基础上引入了一种新的方法,对带一般非线性项的二阶椭圆型方程爆炸解的存在性进行了研究,得到了RN(N≥3)上具有C2有界区域Ω上爆炸解的存在性,进而得到全空间RN(N≥3)上爆炸解的存在性.     

拟线性椭圆型方程组正整体解的存在性

本文讨论了一类满足初值条件的非线性椭圆型方程组正整体解的存在性     

具有非线性梯度项的半线性椭圆型方程的爆炸解

本文在经典摄动方法与椭圆型偏微分方程的估计理论的基础上引入了一种新的方法,对带一般非线性项的二阶椭圆型方程爆炸解的存在性进行了研究,得到了RN(N≥3)上具有C2有界区域Ω上爆炸解的存在性,进而得到全空间RN(N≥3)上爆炸解的存在性.     

非线性椭圆型Haseman边值问题

本文首先给出多个未知复函数的非线性椭圆型复方程组织的非线性Ｈａｓｅｍａｎ边值问题解的估计式，然后使用Ｌｅｒａｙ-Ｓｃｈａｕｄｅｒ定理讨论上述问题的可解性。     

Study of the blow-up of solutions of systems of equations of hydrodynamic type

Mathematical Notes - We study the initial boundary-value problem for three-dimensional systems of equations of pseudoparabolic type. The system is similar to the Oskolkov system, but differs from...     

Characterization of types of asymptotic discernibility of families of hypotheses

We give a characterization of the types of asymptotic discernibility of families of hypotheses in the case of hypothetical measures that are not, in general, mutually absolutely continuous. The case when the logarithm of the likelihood ratio admits an asymptotic expansion of the type of an expansion with local asymptotic normality is examined in detail. Examples are studied.Translated fromTeoriya Sluchainykh Protsessov, Vol. 15, pp. 64–71, 1987.     

Distribution of types of symmetry of tensors of high degree

The asymptotic distribution of tensors of degree N in symmetry types is studied in this paper.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 155, pp. 181–186, 1986.     

Singularities of Solutions of One Class of Equations of Continuum Mechanics

We analyze one class of families of integral equations and describe the dependence of the singularities of solutions of integral equations on the dimensions of the families of kernels of equations. On the basis of these results, we propose procedures for the construction of approximate solutions for a small parameter.     

Determination of asymptotic solutions of problems of nonlinear theories of thermoviscoelasticity

It is shown that the asymptotic solution of a problem of the nonlinear theory of thermoviscoelasticity, if it exists, can be found directly from the solution of the asymptotic boundary-value problem without completely solving the starting problem.M. V. Lomonosov Moscow State University. Translated from Mekhanika Polimerov, No. 3, pp. 395–400, May–June, 1976.     

Emptiness of set of points of lower semicontinuity of Lyapunov exponents

We consider parametric families of differential systems with coefficients that are bounded and continuous on the half-line and uniformly in time continuously depend on a real parameter. For each Lyapunov exponent, we construct a family such that the Lyapunov exponent of its systems treated as a function of the parameter is not a lower semicontinuous function for any value of the parameter.