THE GENERALIZED SINE-GORDEN EQUATIONS AND THEIR GEOMETRIC ASPECTS

§1 INTRODUCTION The work on"Lie group and KDV equations" has been done in[1]. From the structure equations of certain Lie Group, a class of evolution equations of Sine-Gorden type may be achieved. In this paper from a new viewpoint introduced in [2], we will derive a class of evolution equations of Sine-Gorden type. Furthermore we have given geometric interoretations for our evolution equations of Sine-Gorden type. The evolution equations of Sine-Gorden type which have been got in [3] are a special class of our paper.     

具有多奇性的非线性热方程的定解问题

利用Kato类函数和Green胎紧函数的性质得到了具有多奇性的非线性热方程的初值问题和初边值问题．弱解的存在性．     

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证明了具有奇性的一类非线性多调和方程在R^n(n≥3)上的整体正解的存在性和多解性，用两个具体的例子说明定理的应用．     

有界洞型区域内半线性椭圆方程组的正解

利用不动点定理 ,证明了几种半线性椭圆型方程组在洞型区域内正解的存在性与不存在性以及唯一性 ,并给出两个应用实例     

ON THE RADIAL GROUND STATE OF P-LAPLACIAN EQUATION WITH GRADIENT TERM PERTURBATION

1IntroductionInthispaper,weconsidertheexistence,uniqueuessandnonexistenceoftheradialgroundstatetothefollowingp-Laplacianequation:whereApu=div(IDttl)Du),n>p22,qissubcriticalexponents,i.e.,qo.Bydefinition,afunctionu(x)issaidtobetheradialgroundstateto(1.1),ifu(x)=u(r)satisfies:1)u(r),Iu'Ip-'U'eC'([o, oo));2)u(r)isthesolutionofthefollowingCauchyproblem:3)u(r)satisfiesIn0urf0rmerpaper[1],westlldiedtheexistenceanduniqueness0fradialgroundstatetoproblem(1-1)inthecasewhereq…     

加权p-Laplace方程解的整体分叉问题

该文利用指标理论，谱理论以及标准分叉定理，研究了加权索伯列夫空间中的p Laplace方程初值问题的解的整体分叉现象。     

半线性双调和方程奇异位势问题的非平凡解

研究了在四维空间R4中球域B内的半线性奇异双调和方程的Dirichlet边值问题.其中,奇异项中不但含有通常的奇位势,还含有对数权,使得该奇异项成为R4空间中的临界位势.文中首先建立了相应的Hardy不等式,然后通过山路引理得出了该问题非平凡解的存在性.     

双退化拟线性椭圆型方程Keldys-Fichera障碍问题

讨论一类双退化散度型拟线性椭圆型方程的Keldys-Fichera障碍问题,证明了解的存在性.     

THE FIRST BOUNDARY VALUE PROBLEM FOR STRONGLY DEGENERATE QUASILINEAR PARABOLIC EQUATIONS

This paper concerns with existence of generalized solutions of first boundary value problem for a kind of strongly degenerate quasilinear parabolic equations. The author assumes that the coefficients in the equation satisfy strongly degenerate monotone condition and other weakened conditions comparing with those of Ladyzenskaja's. An existence theorem is given and proved.     

高阶Schrdinger方程的特征值问题

本文给出了高阶Ｓｃｈｒｄｉｎｇｅｒ算子的二相邻特征值之间的距离估计，并对其负特征值个数给出一个上界