Invariance stability under perturbed coefficients of Gille-Wȩgrzyn's nonlinear differential equations (Q1110704)

Recent results of \textit{B. R. Barmish} (IEEE Trans. AC-29, 935-936 (1984; Zbl 0549.93046)) and of \textit{S. Bialas} and \textit{J. Garloff} [ibid. AC- 30, 210-213 (1985; Zbl 0555.65010)] on invariance of the strict Hurwitz property of polynomials under perturbations of their coefficients are applied to the stability analysis of a special fourth order nonlinear differential equation (Gille-Wȩgrzyn's equation \(x^{(4)}+a_ 1x^{(3)}f+a_ 2x''+a_ 3x'+a_ 4x=0,\) where \(f=f(x^{(3)},x'',x',x)\) is an arbitrary Lipschitz continuous nonlinear function satisfying \(f\geq 0\) and \(f(0,0,0,0)=0)\).