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Periodic solutions for: (t) = λf(x(t),x(t – 1))

  • O. Arino (a1) and R. Benkhalti (a2)


We present a new result on the existence of periodic solutions for the equation:

for all positive parameters λ sufficiently large. Our fundamental assumption is the following monotonicity property: if ø ≧ ψ (ø and ψ are data) then x(ø) ≧ x(ψ). The proof consists in applying the global Hopf bifurcation theorem. The main steps are: (i) a classical estimation of the periods; (ii) an a priori estimate for the solutions along a connected branch; (iii) a transformation acting on periodic solutions.



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Periodic solutions for: (t) = λf(x(t),x(t – 1))

  • O. Arino (a1) and R. Benkhalti (a2)


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