Multiple positive solutions of a discrete difference system
The authors study the discrete system \[ \Delta^2u_1(k)+f_1(k,u_1(k),u_2(k))=0,\quad \Delta^2u_2(k)+f_2(k,u_1(k),u_2(k))=0, \] \(k\in[0,T]\), with the Dirichlet boundary conditions \[ u_1(0)=u_1(T+2)=0,\quad u_2(0)=u_2(T+2)=0. \] Sufficient conditions for existence of at least three positive solutions to the above boundary value problem are given. The proof is based on the fixed point theorem of \textit{R. W. Leggett} and \textit{L. R. Williams} [Indiana Univ. Math. J. 28, 673-688 (1979; Zbl 0421.47033)].
scientific article; zbMATH DE number 1957187