Variationally stable differential systems
The author studies the stability of the perturbed system \(y'=f(t,y)+g(t,y)\) knowing the stability of the variational system \(z'=f_ x(t,x(t,t_ 0,x_ 0))z\). It is assumed that \(| g(t,y)| \leq \sum^{p}_{i=1}\lambda_ i(t)\omega_ i(| y|)\), where \(\lambda_ i\) are continuous, \(\omega_ i\) are nondecreasing and positive on (0,\(\infty)\) such that \(1/\omega_ i\not\in L_ 1((0,1])\) and \(\omega_{i+1}/\omega_ i\) are nondecreasing functions on (0,\(\infty)\).
scientific article; zbMATH DE number 4200648