MA Shi-wang, WANG Zhi-cheng, YU Jian-she. The Existence of Periodic Solutions for Nonlinear Systems of First-Order Differential Equations at Resonance[J]. Applied Mathematics and Mechanics, 2000, 21(11): 1156-1164.
 Citation: MA Shi-wang, WANG Zhi-cheng, YU Jian-she. The Existence of Periodic Solutions for Nonlinear Systems of First-Order Differential Equations at Resonance[J]. Applied Mathematics and Mechanics, 2000, 21(11): 1156-1164.

# The Existence of Periodic Solutions for Nonlinear Systems of First-Order Differential Equations at Resonance

• Rev Recd Date: 2000-04-12
• Publish Date: 2000-11-15
• The nonlinear system of first-order differential equations with a deviating argument x>(t)=Bx(t)+F(x(t-τ))+p(t),is considered,where x(t)∈R2,τ∈R,B∈R2×2 F is bounded and p(t) is continuous and 2π-periodic.Some sufficient conditions for the existence of 2π-periodic solutions of the above equation,in a resonance case,by using the Brouwer degree theory and a continuation theorem based on Mawhin's coincidence degree are obtained.Some applications of the main results to Duffing's equations are also given.
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