Abstract
In this paper we consider the existence, multiplicity, and nonexistence of positive periodic solutions forn-dimensional nonautonomous functional differential systemx'(t)=H(t,x(t))-λB(t)F(x(t-τ(t))), wherehiareω-periodic intand there existω-periodic functionsαi,βi∈C(R,R+)such thatαi(t)≤(hi(t,x)/xi)≤βi(t),∫0ωαi(t)dt>0,forx∈R+nall withxi>0,andt∈R,limxi→0+(hi(t,x)/xi)exist fort∈R;bi∈C(R,R+)areω-periodic functions and∫0ωbi(t)dt>0;fi∈C(R+n,R+),fi(x)>0forx >0;τ∈(R,R)is anω-periodic function. We show that the system has multiple or no positiveω-periodic solutions for sufficiently large or smallλ>0, respectively.
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