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Multiple positive solutions of a discrete difference system. (English) Zbl 1030.39015
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 {\it R. W. Leggett} and {\it L. R. Williams} [Indiana Univ. Math. J. 28, 673-688 (1979; Zbl 0421.47033)].

39A11Stability of difference equations (MSC2000)
39A12Discrete version of topics in analysis
Full Text: DOI
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