ISSN:
1573-2754
Keywords:
first-order differential equation
;
periodic solution
;
resonance
;
Brouwer degree
;
coincidence degree
;
Duffing equation
;
O175
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
,
Mathematics
,
Physics
Notes:
Abstract The nonlinear system of first-order differential equations with a deviating argument $$\dot x(t) = Bx(t) + F(x(t - \tau )) + p(t)$$ is considered, where x(t)εR 2, τεR, BεR 2×2, 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.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF02459250
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