Periodic Solutions for Delay Lotka]Volterra Competition Systems

By using the continuation theorem of coincidence degree theory, sufficient and realistic conditions are obtained for the existence of positive periodic solutions for the periodic distributed delay Lotka]Volterra competition system dui t. n 0 dt sui t. ri t. yai i t.ui t. y j s1ai j t.HyTi jKi j s.uj tqs. ds , j/i is1, 2, . . . , n, and the periodic state dependent delay Lotka]Volterra competition system dui t. n dt sui t. ri t. yai i t.ui t. y ai j t.uj tyt j t ,u1 t., . . . ,un t..., js1 j/i is1, 2, . . . , n, where ri, aii)0, aijG0 j/i, i, js1, 2, . . . , n.are continuous v-periodic func- tions, Ti jg 0, `. j/i, i, js1, 2, . . . , n., Ki jgC wyTi j, 0x, 0, `.., Hy0Ti jKij s.ds s1 j/i, i, js1, 2, . . . , n., tigC Rnq1, R., and ti is1, 2, . . . , n.are v-periodic with respect to their first arguments, respectively