On positive solutions of some classes of max-type systems of difference equations

Abstract

Global attractivity results on positive solutions of some special cases of the next max-type system of difference equationsxn(i)=max1,xn- l1(i)(i)p1(i)j1=1m1(i)xn-λj1(i1)(sj1(i1))qj1(i1),.,xn-lri(i)(i)pri(i)jri=1m ri(i)xn-λjri( iri)(sjri(iri))qjri(iri),nN0,where riN,i=1,k,kN, sjt(it){1,.,k},qjt(it)≥0, i=1,k,t{1,.,ri} and pj(i)[0,1], mj(i)N,i=1,k,j=1,ri, are presented. We also present some results on the behavior of positive solutions of the difference equation xn=max{p1xn-1,.,pkxn-k}, where pj,j=1,k are nonnegative numbers.