共查询到20条相似文献,搜索用时 31 毫秒
1.
Zhi Ting Xu 《数学学报(英文版)》2008,24(5):829-842
By using the averaging technique, we establish some oscillation theorems for the second order damped elliptic differential equation N↑∑↓i,j=1 Di[AIY(x)Djy]+N↑∑↓i=1 bi(x)Diy+c(x)f(y)=0 which extend and improve some known results in the literature. 相似文献
2.
Zhi-ting Xu 《应用数学学报(英文版)》2009,25(2):291-304
Using general means, we establish several new Philos-type oscillation theorems for the second order damped elliptic differential equation
Σi,j=1 N Di[aij(x)Djy]+Σi=1 N bi(x)Diy+c(x)f(y)=0
under quite general assumptions. The obtained results are extensions of the well-known oscillation results due to Kamenev, Philos, Yan for second order linear ordinary differential equations and improve recent results of Xu, Jia and Ma. 相似文献
Σi,j=1 N Di[aij(x)Djy]+Σi=1 N bi(x)Diy+c(x)f(y)=0
under quite general assumptions. The obtained results are extensions of the well-known oscillation results due to Kamenev, Philos, Yan for second order linear ordinary differential equations and improve recent results of Xu, Jia and Ma. 相似文献
3.
V. Zh. Dumanyan 《Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences)》2010,45(1):26-42
The paper suggests some conditions on the lower order terms, which provide that the solution of the Dirichlet problem for
the general elliptic equation of the second order
$
\begin{gathered}
- \sum\limits_{i,j = 1}^n {\left( {a_{i j} \left( x \right)u_{x_i } } \right)_{x_j } + } \sum\limits_{i = 1}^n {b_i \left( x \right)u_{x_i } - } \sum\limits_{i = 1}^n {\left( {c_i \left( x \right)u} \right)_{x_i } + d\left( x \right)u = f\left( x \right) - divF\left( x \right), x \in Q,} \hfill \\
\left. u \right|_{\partial Q} = u_0 \in L_2 \left( {\partial Q} \right) \hfill \\
\end{gathered}
$
\begin{gathered}
- \sum\limits_{i,j = 1}^n {\left( {a_{i j} \left( x \right)u_{x_i } } \right)_{x_j } + } \sum\limits_{i = 1}^n {b_i \left( x \right)u_{x_i } - } \sum\limits_{i = 1}^n {\left( {c_i \left( x \right)u} \right)_{x_i } + d\left( x \right)u = f\left( x \right) - divF\left( x \right), x \in Q,} \hfill \\
\left. u \right|_{\partial Q} = u_0 \in L_2 \left( {\partial Q} \right) \hfill \\
\end{gathered}
相似文献
4.
Zhi Ting XU 《数学学报(英文版)》2007,23(7):1189-1198
By using vector Riccati transformation and averaging technique, some oscillation criteria for the quasilinear elliptic differential equation of second order,
ΣNi,j=1Di[Ψ(y)Aij(x)|Dy|^p-2Djy]+p(x)f(y)=0,
are obtained. These theorems extend and include earlier results for the semilinear elliptic equation and PDE with p-Laplacian. 相似文献
5.
Zhi-ting Xu 《应用数学学报(英文版)》2007,23(4):569-578
Some oscillation theorems are given for the nonlinear second order elliptic equationsum from i,j=1 to N D_i[a_(ij)(x)Ψ(y)||▽y||~(p-2)D_(jy)] c(x)f(y)=0.The results are extensions of modified Riccati techniques and include recent results of Usami. 相似文献
6.
S. A. Aldashev 《Ukrainian Mathematical Journal》1991,43(4):379-384
For the linear hyperbolic equations $$\sum\limits_{i,j = 1}^{m + 1} {a_{ij} \left( {x,x_{m + 1} } \right)u_{x_i x_j } + \sum\limits_{i = 1}^{m + 1} {a_i \left( {x,x_{m + 1} } \right)u_{x_i } + c\left( {x,x_{m + 1} } \right)u = 0,x = \left( {x_1 ,...,x_m } \right)} ,} m \geqslant 2,$$ the correctness of multidimensional analogues of the problems of Darboux and Goursat is established and a theorem on the uniqueness of a solution of the Cauchy characteristic problem is proved. 相似文献
7.
Let n ≥ 2 be an integer. In this paper, we investigate the generalized Hyers-Ulam stability problem for the following functional equation f(n-1∑j=1 xj+2xn)+f(n-1∑j=1 xj-2xn)+8 n-1∑j=1f(xj)=2f(n-1∑j=1 xj) +4 n-1∑j=1[f(xj+xn)+f(xj-xn)] which contains as solutions cubic, quadratic or additive mappings. 相似文献
8.
Si Ligeng 《数学年刊B辑(英文版)》1982,3(2):203-208
In this paper, we have obtained the equivalence theorems of stability between the system of differential equations
$[{\dot x_i}(t) = \sum\limits_{j = 1}^n {{a_{ij}}{x_j}(t)} + \sum\limits_{j = 1}^n {{b_{ij}}{x_j}(t)} + \sum\limits_{j = 1}^n {{c_{ij}}{{\dot x}_j}(t)} (i = 1,2, \cdots ,n)\]$
and the system of differential-difference equations of neutral type
$[{\dot x_i}(t) = \sum\limits_{j = 1}^n {{a_{ij}}{x_j}(t)} + \sum\limits_{j = 1}^n {{b_{ij}}{x_j}(t - {\Delta _{ij}})} + \sum\limits_{j = 1}^n {{c_{ij}}{{\dot x}_j}(t - {\Delta _{ij}})} (i = 1,2, \cdots ,n)\]$
where a_ij, b_ij, c_ij are given constants, and \Delta_ij are non-negative real constants. 相似文献
9.
We consider the properties on solutions of some q-difference equations of the form ∑ n j=0 aj(z)f(qj z)=an+1(z), where a0(z),..., an+1(z) are meromorphic functions, a0(z)an(z) ≠ 0 and q ∈ C such that 0 〈 |q| ≤ 1. We give estimates on the upper bound for the length of the gap in the power series of entire solutions of (*) when the coefficients a0(z),..., an+1(z) are polynomials and 0 〈 |q| 〈 1. For some special cases, we give estimates of growth of f(z). And we also show that the case 0 〈 |q| 〈 1 is different from the case |q|=1. 相似文献
10.
Hisao Watanabe 《Probability Theory and Related Fields》1988,77(3):359-378
In this paper we consider the parabolic equation with random coefficients:
|