共查询到19条相似文献,搜索用时 156 毫秒
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对超双曲型方程的正确提法还知之不多,著名的Asgeirsson中量定理使得一些定解问题得以解决,而且它可以用来证明超双曲型方程解的拓展性。因此对Asgeirsson中量定理的推广就有重要意义。目前对变数超双曲型方程解的中量性质的研究未取得明确结论。本文针对一类变系数超双曲型方程引入了一种广义中量,利用Green公式,导出了广义中量满足一种广义E-P-D方程,证明了该广义E-P-D方程解的存在性和所具有的正则性,从而对于一类变系数的超双曲型方程,得到了解的中量定理。利用该中量定理,得到了(模)超双曲型方程Cauchy问题的解和超双曲型方程解拓展性及其应用。 相似文献
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本文是超双曲型方程定性研究的一个综合报导,它包括L.Asgeirsson中量定理的一个新证法;中量定理的推广;广义势解的非解析性;解的拓展性,境界值问题;基本解问题。 相似文献
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本文是超双曲型方程定性研究的一个综合报导,它包括 L.Asgeirsson 的中量定理的一个新证法;中量定理的推广;广义势解的非解析性;解的拓展性,境界值问题;基本解问题。 相似文献
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刘家沛 《数学年刊A辑(中文版)》1987,(1)
本文研究超双曲型方程首先建立了广义Asgeirsson中量定理,作为其应用,我们指出在一类特征流型上既推广了著名的Asgeirsson公式,也包含了Hans Lewy的结果接着Huyghens原理被推广到一类超双曲型方程。 相似文献
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刘家沛 《数学年刊B辑(英文版)》1987,(1)
本文研究超双曲型方程首先建立了广义 Asgeirsson 中量定理,作为其应用,我们指出在一类特征流型上既推广了著名的 Asgeirsson 公式,也包含了 Hans Lewy 的结果接着 Huyghens 原理被推广到一类超双曲型方程. 相似文献
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利用Fourier级数理论讨论了一类高阶中立型方程的周期解问题,所得结果改进了司建国(应用数学和力学,第17卷1期:关于高阶常系数中立型方程周期解的讨论)的主要结果,即将该定理1的条件/b0/〈1/2改为/b0/≠1,从而该的其它定理相应得到改进。 相似文献
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一类高阶中立型方程的周期解 总被引:5,自引:0,他引:5
利用Fourier级数理论讨论了一类高阶中立型方程的周期解问题·所得结果改进了司建国(应用数学和力学,第17卷1期:关于高阶常系数中立型方程周期解的讨论)的主要结果,即将该文定理1的条件|b0|<1/2改为|b0|≠1,从而该文的其它定理也可相应得到改进 相似文献
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应用Hille-Yosida定理研究了无穷维Hamilton算子,得到了一个无穷维Hamilton系统初值问题解的存在性定理,并把结果应用在由一类双曲型偏微分方程导出的无穷维Hamilton系统中,给出了此类无穷维Hamilton系统解的存在性定理. 相似文献
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Hari M. Srivastava Anvar Hasanov Tuhtasin Gulamjanovich Ergashev 《Mathematical Methods in the Applied Sciences》2020,43(10):6181-6199
Potentials play an important role in solving boundary value problems for elliptic equations. In the middle of the last century, a potential theory was constructed for a two-dimensional elliptic equation with one singular coefficient. In the study of potentials, the properties of the fundamental solutions of the given equation are essentially and fruitfully used. At the present time, fundamental solutions of a multidimensional elliptic equation with one degeneration line are already known. In this paper, we investigate the double- and simple-layer potentials for this kind of elliptic equations. Results from potential theory allow us to represent the solution of the boundary value problems in the form of an integral equation. By using some properties of the Gaussian hypergeometric function, we first prove limiting theorems and derive integral equations concerning the densities of the double- and simple-layer potentials. The obtained results are then applied in order to find an explicit solution of the Holmgren problem for the multidimensional singular elliptic equation in the half of the ball. 相似文献
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In this paper, by using Avery-Peterson theorem on a convex cone, we consider the m-point boundary value problems for second order impulsive differential equations with the nonlinear term depending on the first order derivative, the multiplicity result of three positive solutions are obtained. 相似文献
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We obtain a differential equation for the spherical means generated by a multidimensional generalized shift of an arbitrary smooth “even” function. We study the Asgeirsson property of solutions of a singular ultrahyperbolic equation that includes singular differential operators Δ B acting in Euclidean spaces, in general, of distinct dimensions. We represent the structure of a “radial” solution of the considered equation. A theorem similar to the Asgeirsson inverse theorem is proved. 相似文献
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Three positive solutions for boundary value problem for differential equation with Riemann-Liouville fractional derivative 下载免费PDF全文
In this paper, by using the Avery-Peterson fixed point theorem, we establish the existence result of at least three positive solutions of boundary value problem of nonlinear differential equation with Riemann-Liouville''s fractional order derivative. An example illustrating our main result is given. Our results complements and extends previous work in the area of boundary value problems of nonlinear fractional differential equations. 相似文献
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Yuji Liu 《Journal of Applied Mathematics and Computing》2012,38(1-2):195-208
Sufficient conditions for the existence of solutions of nonlinear boundary value problems for higher order functional difference equations with p-Laplacian are established by using the continuation theorem. The result is proved without using the monotonicity of B i (i=0,1). We allow f to be at most linear, superlinear or sublinear in obtained results. 相似文献
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Nobito Yamamoto Mitsuhiro T. Nakao Yoshitaka Watanabe 《Numerical Functional Analysis & Optimization》2013,34(11):1190-1204
We give a theoretical result with respect to numerical verification of existence and local uniqueness of solutions to fixed-point equations which are supposed to have Fréchet differentiable operators. The theorem is based on Banach's fixed-point theorem and gives sufficient conditions in order that a given set of functions includes a unique solution to the fixed-point equation. The conditions are formulated to apply readily to numerical verification methods. We already derived such a theorem in [11], which is suitable to Nakao's methods on numerical verification for PDEs. The present theorem has a more general form and one may apply it to many kinds of differential equations and integral equations which can be transformed into fixed-point equations. 相似文献
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In this paper, we consider the boundary value problem with the shift for nonlinear uniformly elliptic equations of second order in a multiply connected domain. For this sake, we propose a modified boundary value problem for nonlinear elliptic systems of first order equations, and give a priori estimates of solutions for the modified boundary value problem. Afterwards we prove by using the Schauder fixedpoint theorem that this boundary value problem with some conditions has a solution. The result obtained is the generlization of the corresponding theorem on the Poincare boundary value problem. 相似文献
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本文利用Monch不动点定理和一个比较结果,研究了实 Banach空间中二阶非线性混合型脉冲积分-微分方程初值问题解的存在性. 相似文献