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Conditions for the existence of solutions converging to zero in the case of homogeneous linear differential equations

✍ Scribed by V. Kertész

Publisher
Elsevier Science
Year
1991
Tongue
English
Weight
336 KB
Volume
21
Category
Article
ISSN
0898-1221

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✦ Synopsis

Suppose the solution x _= 0 is asymptotically stable. This fact can be proved by an appropriate positive definite Lyapunov function. In such cases we always can find a positive function a(t) for which lim a(t) = 0 and | ---*CO

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In this paper we consider the nonlinear third-order quasi-linear differential equation and obtain some simple conditions for the existence of a periodic solution for it. In so doing we use the implicit function theorem to prove a theorem about the existence of periodic solutions and consider one ex