Abstract :
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
Keywords :
Topological degree , competitionsystem , distributed delay , State dependent delay , Periodic solution
