On Nontrivial Solutions of Homogeneous Dirichlet Problem for Partial Differential Equations in a Layer

Z. Nytrebych; V. Ilkiv; P. Pukach; O. Malanchuk

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On Nontrivial Solutions of Homogeneous Dirichlet Problem for Partial Differential Equations in a Layer

机译：层中偏微分方程齐次Dirichlet问题的非平凡解

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We establish the necessary and sufficient conditions of existence of nontrivial quasi-polynomial solutions of the problem in a layer for homogeneous partial differential equation with $s+1$ variables of second order in time variable and generally infinite order in other $s$ (spatial) variables with Dirichlet boundary conditions in time. We apply the differential-symbol method for constructing such quasi-polynomial solutions. We also give examples of problems for which we construct other solutions besides of quasi-polynomial ones.

机译：我们为均质偏微分方程层中存在该问题的非平凡拟多项式解的存在的充要条件，该均质偏微分方程的时间变量为二阶的$ s + 1 $变量，而其他$ s $（空间为二阶变量））具有Dirichlet边界条件的变量。我们应用微分符号方法构造这种准多项式解。我们还给出了一些问题的例子，除了准多项式之外，我们还为其构建了其他解决方案。

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《Kragujevac Journal of Mathematics》 |2018年第2期|共15页
作者
Z. Nytrebych; V. Ilkiv; P. Pukach; O. Malanchuk;
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中图分类数学;
关键词
Differential-symbol methodtwo-point problem for partial differential equationsmultipoint problemequations of mathematical physics;

机译：微分符号法偏微分方程的两点问题多点数学方程组;

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1. Discussion on ????????Numerical solution of 2nd-order hyperbolic partial differential equations by the method of continuous characteristics????????, ????????Analogue solution of 2nd-order hyperbolic partial differential equations by the method of continuous characteristics???????? and ????????Analogue solution of elliptic differential equations by conformal transformations???????? [J] . Electrical Engineers, Proceedings of the Institution of . 1971,第6期

机译：用连续特性方法讨论二阶双曲型偏微分方程的数值解??????，二阶双曲型的模拟解偏微分方程的连续特性方法和利用共形变换的椭圆型微分方程的模拟解
2. CONDITIONS OF NONTRIVIAL SOLVABILITY OF THE HOMOGENEOUS DIRICHLET PROBLEM FOR EQUATIONS OF ANY EVEN ORDER IN THE CASE OF MULTIPLE CHARACTERISTICS WITHOUT SLOPE ANGLES [J] . Buryachenko EA Ukrainian mathematical journal . 2010,第5期

机译：在没有斜坡角的多个特征情况下，偶偶狄立克特方程对任何偶数方程的非可解性的条件
3. Some aspects of the nontrivial solvability of homogeneous Dirichlet problems for linear equations of arbitrary even order in the disk [J] . V. P. Burskii, E. A. Buryachenko Mathematical notes . 2005,第3a4期

机译：圆盘上任意偶数阶线性方程组齐次Dirichlet问题非平凡可解性的某些方面
4. Nontrivial Solutions of Singular Sign-Changing Nonlinear Dirichlet-Type Fractional Differential Equation [C] . Cao Xilin 2011 Asia-Pacific Power and Energy Engineering Conference . 2011

机译：奇异符号改变非线性Dirichlet型分数阶微分方程的非平凡解
5. Holomorphic extension of solutions to homogeneous analytic partial differential equations. [D] . Armel, Jonathan J. 2009

机译：齐次解析偏微分方程解的全纯扩展。
6. Invariant Differential Forms in Several Group Variables as Solutions of Partial Differential Equations in Fréchet Differentials [O] . Aristotle D. Michal 1951

机译：Fréchet微分方程中偏微分方程解的几个组变量的不变微分形式
7. Absence of nontrivial solutions for a class of partial differential equations and systems in unbounded domains [O] . Akrout K., Khodja B. 2009

机译：无界域中一类偏微分方程和系统的非平凡解的存在
8. On the Nonpropagation of Zero Sets of Solutions of Certain Homogeneous Linear Partial Differential Equations across Noncharacteristic Hyperplanes [R] . Cohoon, D. K. 1981

机译：非特征超平面上一类齐次线性偏微分方程零解的非传播性

On Nontrivial Solutions of Homogeneous Dirichlet Problem for Partial Differential Equations in a Layer

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