On constant-sign solutions of a system of discrete equations
On constant-sign solutions of a system of discrete equations
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关于离散方程组的常符号解
DOI：
10.1016/0377-0427(86)90127-5
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发表时间：
1986
期刊：
影响因子：
--
通讯作者：
P. J. Wong
中科院分区：
文献类型：
--
作者：
R. Agarwal;D. O’Regan;P. J. Wong
我们考虑如下离散方程组$$u_i (k) = \sum\limits_{\ell = 0}^N {g_i (k,\ell )fi(\ell ,u_1 (\ell )} ,u_2 (\ell ), \cdots ,u_n (\ell )), k \in \{ 0,1, \cdots ,T\} ,$$ 1≤i≤nwhereT≥N>0, 1≤i≤N。建立了系统单、双、多常符号解的存在性判据。为了说明所得结果的普遍性，我们将其应用于几个众所周知的边值问题。并将上述系统推广到在{0,1，…}$$u_i (k) = \sum\limits_{\ell = 0}^\infty {g_i (k,\ell )fi(\ell ,u_1 (\ell )} ,u_2 (\ell ), \cdots ,u_n (\ell )), k \in \{ 0,1, \cdots \} ,1 \leqslant i \leqslant n$$上，研究了常符号解的存在性。
We consider the following system of discrete equations $$u_i (k) = \sum\limits_{\ell = 0}^N {g_i (k,\ell )fi(\ell ,u_1 (\ell )} ,u_2 (\ell ), \cdots ,u_n (\ell )), k \in \{ 0,1, \cdots ,T\} ,$$ 1≤i≤nwhereT≥N>0, 1≤i≤n. Existence criteria for single, double and multiple constant-sign solutions of the system are established. To illustrate the generality of the results obtained, we include applications to several well known boundary value problems. The above system is also extended to that on {0, 1,…} $$u_i (k) = \sum\limits_{\ell = 0}^\infty {g_i (k,\ell )fi(\ell ,u_1 (\ell )} ,u_2 (\ell ), \cdots ,u_n (\ell )), k \in \{ 0,1, \cdots \} ,1 \leqslant i \leqslant n$$ for which the existence of constant-sign solutions is investigated.