Oscillation Property for the Eigenfunctions of Discrete Clamped Beam Equation and Its Applications  

作　　者：Yanqiong LU Rui WANG 

机构地区：[1]College of Mathematics and Statistics,Northwest Normal University,Gansu 730070,P.R.China

出　　处：《Journal of Mathematical Research with Applications》2021年第4期401-415,共15页数学研究及应用（英文版）

基　　金：Supported by the National Natural Science Foundation of China(Grant Nos.11901464;11801453);the Young Teachers’Scientific Research Capability Upgrading Project of Northwest Normal University(Grant No.NWNULKQN2020-20).

摘　　要：In this article,we established the structure of all eigenvalues and the oscillation property of corresponding eigenfunctions for discrete clamped beam equation △^(4)u(k-2)=λm(k)u(k),k∈[2,N+1]Z,u(0)=△u(0)=0=u(N+2)=△u(N+2)with the weight function m:[2,N+1]Z→(0,∞),[2,N+1]_(Z)={2,3,...,N+1}.As an application,we obtain the global structure of nodal solutions of the corresponding nonlinear problems based on the nonlinearity satisfying suitable growth conditions at zero and infinity.

关 键 词：EIGENVALUE EIGENFUNCTIONS oscillation property bifurcation point nodal solutions 

分 类 号：O241.6[理学—计算数学]