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Vietnam Journal of Mathematics 37:1 (2009) 35-41 

Boundedness of Solutions for a Class of Liénard Equation with Multiple Deviating Arguments

Yuehua Yu and Bing Xiao

Abstract.  Consider the Liénard equation with multiple deviating arguments

x''(t) + f1(x(t))(x'(t))2 + f2(x(t))x'(t) + g0(t, x(t)) + (t, x(t - τj(t))) = p(t),

where f1, f2: R  - > R, and g1, g2: R2  - > R are continuous functions, R = (-∞, +∞),  τj(t)  0,  j = 1,2, ... m  are bounded continuous functions on R, and p(t) is a bounded continuous function on R+ = [0,+∞). We obtain some new sufficient conditions for all solutions and their derivatives to be bounded, which substantially extend and improve important results in the literature.

2000 Mathematics Subject Classification: 34C25, 34K13, 34K25.

Keywords: Liénard equation, deviating argument, boundedness.

 

 

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