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

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.