奇异离散一阶周期系统的多重非负解

Multiplicity of nonnegative solutions to frist order singular discrete periodic systems

研究了奇异离散一阶周期系统{Δx(i)=x(i)[a_1(i)-f_1(i,x(i),y(i))],Δy(i)=y(i)[a_2(i)-f_2(i,x(i),y(i))],ak(i+T)=ak(i),fk(i+T,x,y)=fk(i,x,y),i∈(-∞,+∞),k=1,2;T>0的多重非负解的存在性,其中非线性项fk(i,x,y)(k=1,2)在点(x,y)=(0,0)处具有奇性.并利用锥不动点定理证明了在适当的条件下这个问题至少存在两个解.

This paper is devote to establish the multiplicity of nonnegative solutions to first order singular discrete periodic systems {Δx（i）=x（i）[a1（i）-f1（i,x（i）,y（i））],Δy（i）=y（i）[a2（i）-f2（i,x（i）,y（i））],ak（i＋T）=ak（i）,fk（i＋T,x,y）=fk（i,x,y）,i∈（-∞,＋∞）,k=1,2;T〉0 where the nonlinear term fk （i, x, y ）（ k = 1,2） may be singular at （x, y ） = （0,0）. It is proved that such a problem has at least two nonnegative T-periodic solutions by using fixed point theorem in cones under our reasonable conditions.