Non-continuation results for generalized Liénard differential systems. (English) Zbl 0699.34006
The paper studies the non-continuability of solutions to the differential system: \(x'=f(t,x)\), \(f\in C(I\times {\mathbb{R}}^ n,{\mathbb{R}}^ n)\). Applications to the systems (2.1) and (2.2), i.e., respectively
\[
(2,1)\quad x'=y-F(x),\quad y'=-g(x)k(y)
\]
\[ (2.2)\quad x'=h(y)- F(x),\quad y'=-g(x)k(y) \] are investigated.
\[ (2.2)\quad x'=h(y)- F(x),\quad y'=-g(x)k(y) \] are investigated.
Reviewer: N.Lunge
MSC:
34A12 | Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations |