Multiple positive solutions of BVPs for third-order discrete difference systems.
The paper deals with the system \[ \Delta^3 u_1(x)+ f_1(k, u_1(k), u_2(k))= 0,\quad \Delta^3 u_2(k)+ f_2(k, u_1(k), u_2(k))= 0,\quad 0\leq k\leq T, \] subject to \(u_i(0)= u_i(1)= u_i(T+ 3)= 0\) for \(i= 1,2\). By means of a fixed point theorem due to \textit{R. W. Leggett} and \textit{L. R. Williams} [Indiana Univ. Math. J. 28, 673--688 (1979; Zbl 0421.47033)] the existence of three positive solutions is proved under suitable conditions.
scientific article; zbMATH DE number 2056083