Existence of positive solutions of BVPs for third-order discrete nonlinear difference systems
The following boundary value problem is considered \[ \begin{gathered} \Delta^3 u_1(k)+ f_1(k, u_1(k), u_2(k))= 0,\quad k\in [0,T],\\ \Delta^3 u_2(k)+ f_2(k, u_1(k), u_2(k))= 0,\quad k\in [0,T],\\ u_1(0)= u_1(1)= u_1(T+ 3)= 0= u_2(0)= u_2(T+ 3).\end{gathered} \] New results of the existence, nonexistence and multiplicity are obtained using Krasnosel'skij's fixed point theorem in a cone. In particular, it is proved that the above boundary value problem has \(N\) positive solutions under suitable conditions, where \(N\) is an arbitrary, positive integer.
scientific article; zbMATH DE number 2117977
scientific article