On the asymptotic behavior of solutions of certain non-autonomous differential equations
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In this paper, the authors considered non-autonomous (1.2) third-order differential equations, where a(t, b(t)y c(t), g, h, p are continuous real-valued functions depending only on the arguments shown.Abstract:
(1.2) x+a(t)f(x, Λ, x)x+b(t)g(x9 x)+c(t)h(x) = p(t, x, i, x) where a(t), b(t)y c(t) are positive continuously differentiate and /, g, h, p are continuous real-valued functions depending only on the arguments shown, and the dots indicate the differentiation with respect to t. The asymptotic property of solutions of third order differential equations has received a considerable amount of attention during the past two decades, particularly when (1.2) is autonomous. Many of these results are summarized in [11]. A few authors have studied non-autonomous third order differential equations. K. E. Swick [13] considered the following equationsread more
Citations
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References
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Perturbing uniform asymptotically stable nonlinear systems
Aaron Strauss,James A. Yorke +1 more
TL;DR: In this paper, it is shown that the zero function is not a solution of the solution of a uniform asymptotic stability problem in the case of a single UAV.
Journal ArticleDOI
Stability results for the solutions of some third and fourth order differential equations
TL;DR: In this paper, conditions under which solutions of the equations (1) and (2) of § 1.1 tend to zero as t → ∞ were investigated, where t is the length of the shortest path.