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Zbl 1235.34186
Tunç, Cemil
Asymptotic stable and bounded solutions of a kind of nonlinear differential equations with variable delay. (English)
[J] Funct. Differ. Equ. 17, No. 3-4, 345-354 (2010). ISSN 0793-1786

Summary: By means of a Lyapunov functional, we investigate stability and boundedness of solutions to the nonlinear third order differential equation with variable delay: $$\multline x'''(t)+f(x(t),x'(t),x''(t),x(t-r(t)),x'(t-r(t)), x''(t-r(t)))x''(t)\\ +bx'(t)+g(x(t-r(t)))=p(t,x(t),x'(t),x(t-r(t)),x'(r-r(t)), x''(t)).\endmultline$$ An example is given to illustrate the importance of results obtained.

MSC 2000:: *34K12 Properties of solutions of functional-differential equations

Keywords: stability; boundedness; Lyapunov functional; nonlinear third order differential equations with variable delay

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