Solvability of second-order \(m\)-point difference equation boundary value problems on infinite intervals
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Authors
Changlong Yu
- College of Sciences, Hebei University of Science and Technology, Shijiazhuang, 050018, Hebei, P. R. China.
Jufang Wang
- College of Sciences, Hebei University of Science and Technology, Shijiazhuang, 050018, Hebei, P. R. China.
Yanping Guo
- College of Sciences, Hebei University of Science and Technology, Shijiazhuang, 050018, Hebei, P. R. China.
Surong Miao
- College of Sciences, Hebei University of Science and Technology, Shijiazhuang, 050018, Hebei, P. R. China.
Abstract
In this paper, we study second-order \(m\)-point
difference boundary value problems on infinite intervals
\[
\left\{\begin{array}{l}
\Delta^{2}x(k-1)+f(k,x(k),\Delta x(k-1))=0,~k\in N,\\
x(0)=\sum\limits_{i=1}^{m-2}\alpha_{i}x(\eta_{i}),~\lim\limits_{k
\rightarrow\infty }\Delta x(k)=0,
\end{array}
\right.
\]
where \(N=\{1,2,\cdots\},\ f:N\times R^{2}\rightarrow R\)
is continuous, \(\alpha_{i}\in
R,~\sum\limits_{i=1}^{m-2}\alpha_{i}\neq1,~\eta_{i}\in
N,~0<\eta_{1}<\eta_{2}<\cdots<\infty\) and
\[\Delta x(k)=x(k+1)-x(k),\]
the nonlinear term is dependent in a difference of lower order on
infinite intervals. By using Leray-Schauder continuation theorem,
the existence of solutions are investigated. Finally, we give one
example to demonstrate the use of the main result.
Share and Cite
ISRP Style
Changlong Yu, Jufang Wang, Yanping Guo, Surong Miao, Solvability of second-order \(m\)-point difference equation boundary value problems on infinite intervals, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 11, 5734--5743
AMA Style
Yu Changlong, Wang Jufang, Guo Yanping, Miao Surong, Solvability of second-order \(m\)-point difference equation boundary value problems on infinite intervals. J. Nonlinear Sci. Appl. (2017); 10(11):5734--5743
Chicago/Turabian Style
Yu, Changlong, Wang, Jufang, Guo, Yanping, Miao, Surong. "Solvability of second-order \(m\)-point difference equation boundary value problems on infinite intervals." Journal of Nonlinear Sciences and Applications, 10, no. 11 (2017): 5734--5743
Keywords
- Difference equation
- boundary value problem
- Leray-Schauder continuation theorem
- infinite interval
MSC
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