共查询到20条相似文献,搜索用时 703 毫秒
1.
M. N. Yakovlev 《Journal of Mathematical Sciences》1996,79(3):1146-1149
Let $\gamma ,\delta \in \mathbb{R}^n $ with $\gamma _j ,\delta _j \in \{ 0,1\} $ . A comparison pair for a system of equations fi(u1,…,un)=0 (i=1,…,n) is a pair of vectors $v,w \in \mathbb{R}^n ,v \leqslant w$ , such that $$\begin{array}{*{20}c} {\gamma _i f_i (u_1 , \ldots ,u_{i - 1} ,v_i ,u_i + 1, \ldots ,u_n ) \leqslant 0,} \\ {\delta _i f_i (u_1 , \ldots ,u_{i - 1} ,w_i ,u_i + 1, \ldots ,u_n ) \geqslant 0} \\ \end{array} $$ for $\gamma _j u_j \geqslant v_j ,\delta _j u_j \leqslant w_j (j = 1, \ldots ,n)$ . The presence of comparison pairs enables one to essentially weaken the assumptions of the existence theorem. Bibliography: 1 title. 相似文献
2.
S. S. Khloponin 《Mathematical Notes》1976,20(5):933-938
We have proved that if the partial numerators of the continued fraction f(c)=1/1+c2/l+c3/l+... are all nonzero and for at least some number n?1 satisfy the inequalities $$p_n \left| {1 + c_n + c_{n + 1} } \right| \ge p_{n - 2} p_n \left| {c_n } \right| + \left| {c_{n + 1} } \right|(n \ge 1,p_{ - 1} = p_0 = c_1 = 0,p_n \ge 0),$$ then f(c) converges in the wide sense if and only if at least one of the series $$\begin{array}{l} \sum\nolimits_{n = 1}^\infty {\left| {c_3 c_5 \ldots c_{2n - 1} /(c_2 c_4 \ldots c_{2n} )} \right|} , \\ \sum\nolimits_{n = 1}^\infty {\left| {c_2 c_4 \ldots c_{2n} /(c_3 c_5 \ldots c_{2n + 1} )} \right|} \\ \end{array}$$ 相似文献
3.
M. N. Yakovlev 《Journal of Mathematical Sciences》1989,47(6):2936-2951
For system of integrodifferential equation
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4.
Werner Raab 《Monatshefte für Mathematik》1997,123(1):71-84
The integral $$\int_{\Delta (x)} {u_1^{p_1 ^{ - 1} } ...u_n^{p_n ^{ - 1} } (1 - u_1 - ... - u_n )^{q - 1} du_1 \wedge ... \wedge du_n } $$ extended over then-simplex $$\Delta (x) = \{ (u_1 ,...,u_n ) \in R_ + ^n :u_1 /x_1 + ... + u_n /x_n< 1\} $$ is considered as a natural generalization of the classical incomplete Beta-functionB x (p, q). The partial differential equations of this multivariate incomplete Beta-function lead to a kind of ‘minimum principle’ for its restriction to the hypersurface with the equation:p 1/x 1+...+ +p n /x n =c=const. 相似文献
5.
Kazunaga Tanaka 《Annali di Matematica Pura ed Applicata》1992,162(1):43-76
We study the existence of forced vibrations of nonlinear wave equation:
6.
We prove that blowing up solutions of the system
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