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§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. 相似文献
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1IntroductionInthispaper,weconsidertheexistence,uniqueuessandnonexistenceoftheradialgroundstatetothefollowingp-Laplacianequation:whereApu=div(IDttl)Du),n>p22,qissubcriticalexponents,i.e.,q
o.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… 相似文献
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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。 相似文献
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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. 相似文献
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陈祖墀 《数学物理学报(B辑英文版)》1990,(1)
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. 相似文献
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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 相似文献
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1.IntroductionCanyouheartheshapeofadrum?ProfessorProtteraskedinhisrevisitedpaperrll'Usually,thiskindofproblemscanmathematicallybesolvedbyestimatingtheboundsoftheeigenvaluestopolyharmonicoperators.IfonestrikessimultaneouslyNdrumsmadebythesamematerialandpossessingthesamesize,weshouldaskthatcanyouheartheshapeofthedrums?Toanswerthisquestion,onemightconsideraneigenvalueproblemforacertainsystemasfollows:wherefiisaboundedsmoothdomaininRe(m22),u=(al)ro,'',urn)istheoutwardunitnormaltotheboundaryoffi… 相似文献
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1IntroductionInthispaper,weconsiderthesolvabilityofsingularonedimensionalpLaplacian-likeequationwithNeumannboundaryconditionswhereA(()ispositivefor(>0,h(t)EL'([0,1]),gisacontinuousfunctiondefinedon(--co,0)U(0, co)suchthatg(f)-0asf'l-cojg(()- coas(-0 ,g(()---coas(-0--,andg(')(>0for'/0.Afunctionu(t)issaidtobeasolutionof(1.1),ifthefollowingconditionsaresatisfied:Itiseasytoseethatthenecessaryconditionfortheexistenceofthesolutionof(1.1)isInfact,fromtheassumptionsong,weknowthatu(t)/0foralltE(0,1)… 相似文献
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本文考查一个拟线性障碍问题,其系数具更高的增长阶,且边界条件是Keldys-Fichera型 相似文献
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本文研究奇异半线性抛物方程ut-Δu+V1(x)u=V2(x)up,x∈Rn\{0},t>0的Cauchy问题解的存在性.这里,V1(x),V2(x)可以在原点具有奇性.利用Kato类函数和Green tight函数及不动点定理证明了问题存在正的奇异解,它在原点具有奇性. 相似文献