Solvability of second-order \(m\)-point difference equation boundary value problems on infinite intervals


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.


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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


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